Regarding the First Fall of Stormwind
The first fall of Stormwind occurred when Varian Wrynn was a young man. So this was Varian's first encounter with the Orcs. Now mind you, this Orcish Horde had no justification for the war. They were not being driven from land, they were not starving or lost, nor were they addressing some ancient affront by the Human race. No, these Orcs were foreign invaders from another dimension
Consider, also, how they eventually razed Stormwind. They were able to do so by way of Garona, a Half-Orc assassin acting on behalf of the Horde. So Varian not only saw that the Orcish Army was a mindlessly violent army bent on the destruction of the human race, but that the one Orc who might have been different, the one Orc who appeared to have befriended humanity and proven that not how all Orcs were mindless beasts, betrayed them and proved herself an enemy to humanity by murdering Varian's beloved Father.
Horde apologists will tell you that Garona was acting under mind control. There's two problems with this. First, Varian has no real way of knowing Garona was mind-controlled at the time. All he knows is that an Orc gained the trust and friendship of his father, then used it to betray and murder him, causing the downfall of his kingdom and very nearly the downfall of all humanity. Secondly, Garona was still under the control of the Shadow Council, which was at the time solely an Orcish organization and the de facto leadership of the Horde. Either way, it was the Horde who killed his father and nearly wiped out his people.
On Varian's loss of his second father and Humanity's loss of their greatest Hero
Now, consider the aftermath of this incident. It was Anduin Lothar who saved what remained of Stormwind's people after the razing. He spirited Varian away to Lordaeron along with the rest of the survivors. Once in Stormwind, he replaced Llane as Varian's father figure and mentor, and worked with King Tereneas to establish the Alliance, the force that became the only hope of humans, dwarves, and elves against the Orcish Horde.
And yet, Anduin Lothar was killed in cold blood by the Orcs during their attempt to finish what they had started at Stormwind, killed by Orgrim Doomhammer himself.
Horde Apologists will argue that Orgrim Doomhammer was not under the influence of the Burning Legion, and that he was doing it in self-defense, but again, there's problems with those who insist on this. First, while Orgrim was a friend of Durotan and supposedly had heeded his warning that Blackhand and Gul'dan did not have the Horde's best interests in mind, he still allowed Gul'dan to live, employed his necromancers and the Death Knights in battle, and continued the Horde's genocidal campaign against the the Humans. This all strongly implies that Orgrim was more interested in his own personal power, or at least the dominance of the Orcs, rather than doing what was right.
Regardless, whether Orgrim was under the control of the Burning Legion or not, he was still acting as an enemy of the Alliance. In addition, while the forces of the Alliance did have the Horde pinned down at Blackrock Spire, there was no attempt by Doomhammer to parlay. Instead, he went out to kill.
A Note should be made here that in the original events of Warcraft II, Lothar came to Blackrock under a flag of truce to offer terms of surrender to Orgrim, but was ambushed and killed in Cold Blood by Orgrim's order. A retcon changed this to put Lothar and Orgrim in single combat, but the basic crimes of Orgrim remain, and later depictions of the battle (for example, in the d20 Warcraft games player's guides) have left the circumstances of the single combat murky enough that an ambush or deliberate drawing out of Lothar on the part of Orgrim may have still happened.
Regardless of the exact cause of Lothar's death, the point remains that Orgrim, no matter what his ultimate loyalties, continued the genocidal campaign of the Horde upon the Humans, Dwarves, and High Elves, and killed Anduin Lothar in the process. The Horde killed Humanity's greatest hero and Varian's mentor and second father during an unjust war of genocide against Varian's people, the people he was sworn to protect as King. Thus, the injustices perpetrated against Varian by the Horde continue to stack to unbelievable, unwieldy heights.
On the formation of the New Horde and their attitude toward the Alliance
Horde apologists will argue that all of these problems are the Old Horde, and that the New Horde should be treated as a new, separate entity. Once again, there are very definite problems with this view. Not only are most of the Orcs that make up the current Horde the same Orcs who were the rank and file and leaders of the Old Horde, the fact remains that the New Horde is still using many of the trappings and philosophies of the Old Horde, and is more and more committing new violent acts of their own.
To start with, on the most basic of levels, Thrall continues to use symbology and symbols for the Horde that are, in Human experience, most clearly and basically connected with the Old Horde that was attempting to wipe out the free peoples of Azeroth.
The very title "Warchief" is said to be an ancient title of the Orcs. However, current lore suggests that the title had fallen out of use, and was only taken up again by Rend Blackhand as a tool by Gul'dan to unite the clans as an army of darkness and death. Orgrim Doomhammer took over the title, but continued to use it as the head of a genocidal army. Thrall now claims the title, but the fact remains that, ancestral ties or not, it has been most recently used as a tool of the Burning Legion, only very vaguely tied in to the heritage of an old line of Warchiefs that may or may not have existed, a history that Thrall, as of yet, shows few signs of trying to uncover. When Thrall uses the title Warchief, it is most clearly being used to evoke the power and authority of Orgrim Doomhammer.
Yes, Thrall and the Horde still revere Orgrim Doomhammer, the bloody Warchief who killed Anduin Lothar, the savior of humanity. He is considered a Hero, so much that Thrall wears his armor and carries his hammer - the same Hammer that killed Lothar, or one very similar to it. Thrall calls for peace while wearing the armor and weapon of an Orc who very nearly destroyed Humanity, ostensibly to honor him. In addition, he calls his capital, the symbol of the power and might of the new Horde, Orgrimmar. It's not very hard to see why a human, dwarf, or High Elf might find this symbology a bit insulting, and wonder why the "New" Horde is so eager to honor the Orc who committed some of the worst atrocities of the "Old" Horde. It's even worse for Varian, considering how close he was to Lothar, who was murdered by Orgrim.
Orgrim certainly isn't the only one to be honored like this either. Many of the main generals and architects of the Human, Dwarven, and High Elven genocide are now revered and honored by the Horde, with little to no attempts made to acknowledge their faults and the very real war crimes they committed against the Alliance. Grom Hellscream was one of the first to drink the Demon's blood offered by Gul'dan and commited many atrocities against the Draenei, against humans in the second war, and against Night Elves later.. Kargath Bladefist likewise has had multiple landmarks and fortresses named in his honor, and when he was killed in Outland after revealing himself to be a continued servant of demonic powers, Nazgrel (Another war criminal of the "Old" Horde) spoke of him with respect and honor.
If you are trying to break away from the example of the Old Horde, embracing so much of it seems like a very counter-intuitive way of doing it, and Varian, having at least seen the way Orgrim himself is honored, has a right to at least be made uncomfortable by this.