Is it normal to attempt to fit in society and can't?

Of course it's normal to want. Don't think you aren't capable either. I have a cousin with asperger's syndrome and as far as I'm concerned he's better at socializing than me. Who knows I might have it too. I can fit in. Even if I feel like I can't possibly ever be part of something, a team, a family, somehow I manage, just barely and then some. You probably need to hear from someone who has asperger's syndrome though. Wish you the best, anyway.

Some are just not built to fit into society. We are called Bohemians. We do quite well in our own way, but the simple things most can do without a problem, just do not suit us. I have made a life, living it on my own terms, and it has worked out well enough for me. I've rarely worked 9 to 5, preferring to work 24/7 until I quit and find another job, with as much as a few years between jobs. Never had a vacation, a home and often I've not even owned a vehicle, usually renting one on my bosses nickle. You need not feel guilty or that it is bad to be different; there are plenty of productive people who do not fit the mold of "normal" and do just fine.
Perhaps this is no value to you with your Asperger's syndrome, or maybe it will help.

It's normal for aspies. I function fine on my own and even with casual socialization, but I haven't been able to figure out how society works.