Edit: this got asked a lot, so I'll all a related question instead. Is it possible for a burger to have "good taste and good texture" but also not remind you of beef?
Try a turkey burgers, a chicken burger, a black bean burger, ect... There's so much better variety in veggie burgers, (and they don't cause the run to the bathroom, if you know what I mean.)
And, if you ever find yourself in India, try McDonald's vegetarian burgers. Nothing like beef, but still delicious.
Think of a "burger" as a style of sandwich. Some of us are so used to "hamburger" that it's hard to imagine the patty being anything else.
Honestly, it's worth trying a veggie burger. (A lot of people order them with bacon on top.) As long as you stay away from the "I can't believe it's not meat" style, they're delicious.
Ugh. As someone who hates catsup and mustard, I hate the "it tastes the same when it's loaded with sauce" veggie burgers.
The patties actually need to taste good on their own.
Only of tangential relevance, but maybe still interesting: there's no ham in a traditional hamburger.
The name seems to be derived from the German city of Hamburg.
I've heard plenty of anecdotes of recent immigrants / tourists to the US ordering a "hamburger" expecting it to be ham. It's a rather awkward surprise for Indians who will eat pork, but not beef.
(The downvotes are unfair, IMO.)
Ever had a turkey burger? The meat has a different taste and texture from beef, but it's not bad.
Also see alligator, elk, deer, chicken sausage, etc. "Exactly like beef" is not the end-all-be-all of "satisfyingly meaty", even when you only include actual meat.
Yes! I had one today for dinner in fact. The one I ate today the patty was made with mushrooms, tempeh, and wheat berry. Greens, aioli, pickes & pickled vegetables on top.
Impossible is a blessing because I can be a boring eater and still do ad little harm as possible.
(Being a picky eater sucks. I wish I liked food. I promise, it's not because I like being a pain. My policy is that I'll try anything twice, to avoid any initial bias. I'm just kind of broken.)
I feel like there's a really big hump to get over with expanding a pallet, where once you have even just one or two new foods under your belt it becomes easier to learn to like other ones. For me, it was (and still is) kind of a snowball effect. I'm eating more variety of food now than I ever ate before, but I'm still a lot more narrow than other people I know.
I spent a relatively large portion of my adult life trying to learn to eat vegetables, and it wasn't until midway through transitioning to a vegetarian that I suddenly discovered the magic of sauteing with a little butter and salt instead of boiling vegetables until they were all soft and waterlogged and horrible, or baking them until they just turned into hot mush. That was honestly kind of surreal -- years of not liking veggies, and occasionally trying them in different recipes to see if something had changed, and not having anything change. And then in the space of a few weeks suddenly very quickly realizing that crunchy string beans with a tiny bit of soy sauce were delicious and that I really wanted more food like that.
That's not to say you would like the same stuff. The point is, learning to eat more things is hard, and being a picky eater is hard, and just in case you're stressed about it, don't stress about it. Just keep trying at your own pace and don't worry too much. As long as you keep occasionally experimenting, eventually you'll find a few things you like, and your pallet will expand from there.
And even if you stay a picky eater, as long as you're still getting a decent nutritional intake, and assuming you're meeting whatever dietary goals you have, then you're fine.