I'm terrible at maths which is why I'm not good with physical chem. If you're good at maths then I'd say you'll like physical chem lab cuz its all about using mathematical equations to derive things from your results. Yeah analytical is good fun. We've mainly been learning to do various chromatography methods but we did some atomic absorption spectrophotometry which is pretty cool. Your TA obviously can't do the job hes been assigned. Students should be encouraged to learn from their mistakes, not to blindly follow a lab manual without knowing what they're actually doing. All real chemists have made the mistakes and learned from them. Last year in organic chem lab I completely lost my product at least twice. Once I forgot to check to see that the sep funnel was closed. Another time I added way too much drying agent and it absorbed everything, including my product. The lab techs didn't care because they know that students are there to learn, not produce compounds.
EDIT: Actually now that I think of it, the lab tech did give me a bit of s#*$ for that drying agent incident. I told him what I told you "I'm here to learn" and he couldn't help but agree with me lol. Don't wanna be arrogant but I'd say I'm the most skilled chemist in my class because I'm not afraid to make mistakes and learn from them. They did a kinda surprise test at the end of my org chem lab last year where they got everyone to work by themselves and recrystallise an unknown compound. I was finished 2 hours into the lab. The rest of the class were there for most of the day, the majority of them couldn't even get their compound to recrystallise. I gained that experience through trial and error, not blindly following instructions from a lab manual. Moral of the story: you might as well make the mistakes now while your a student, that way when you're actually in the industry you'll already have the skills.