Fixed your post for you. You're welcome.
The H2 is absolutely the reason why Hummer failed. Just because it was initially met with favorable sales — and may have even given some buyers what they thought they wanted initially — does not mean it wasn't responsible for severely damaging the image of the brand in the bigger picture. (See also: Chevy Citation.)
Not unlike Jeep, Hummer was a brand that built its image around its military heritage and a reputation for building off-road vehicles that were quality, tough, and maybe even a little innovative. They were also recognized for being flashy and expensive; not because they were exactly luxurious, but because of their no-expense-spared, military-grade engineering and design. The model responsible for that creating image was obviously the original civilian-spec AM General Hummer, that would be known as the H1 when GM came into the picture (along with its mil-spec M998 relatives). (To say the civilian-spec Hummer/H1 was the exotic or "Ferrari" of the off-road world in the 90s really wouldn't be wrong.)
When GM launched the H2, the public likely wasn't expecting any addition to the Hummer lineup to be lavishly luxurious, or even comfortable, but they certainly were expecting it to be exceptional off-road and look tough doing it. That's the image the H1 helped build for the brand, remember. The H2, then, would prove to be a textbook example of "appearances only running skin deep."
While the H2 may have worn styling inspired by the H1, under the skin it was hardly anything like its forebearer, thanks in part to GM basing the design heavily on its full-sized truck and SUV platform. It might have been more capable off-road than the Tahoe it was derived from, sure. But what isn't, really? A Tahoe is not and has not been a number one choice for anyone in the off-roading community, as far as I can tell.
It didn't take long for the world to eventually wise up and realize what the H2 actually was — a big, dumb SUV with a chintzy interior, stupid price tag and offensive fuel economy that proved to be borderline, if not completely cumbersome off-road (depending on where you were taking it). It didn't live up to what the brand promised and it not only cast an ugly shadow down on the models it built that were actually OK, like the H3, but also cast one back on the H1.
And, yes, H2 was pretty cumbersome off-road because of its size and design.
Off-road, the H1 (obviously) and even the smaller H3 would humiliate it. The H1 was designed to maintain a low center of gravity while offering superior approach and departure angles and 16 inches of ground clearance. The fact the H2's design borrowed so heavily from the GM truck parts bin meant that this quality would never be replicated. The H3 trounced the H2 off-road by just being plain-old smaller, and it also offered the same amount of ground clearance or better. (It should be said, the final design for H3's chassis also had far less in common with the GM mid-size trucks it had sprung from, especially when compared to the H2 and it's relationship to GM's full-sized truck designs.)
Looking at the bigger picture, GM was better off making the Hummer line-up the H1 (and limiting production to 1,000 units annually until it was totally unprofitable to certify it), the H3 and a production version of the HX concept. They also would have been better off selling Hummer models through GMC dealerships from the very beginning, instead of investing and wasting money setting up standalone lots.