I used to start and stop series all the freaking time. Luckily I've learned how to spot pretty quickly whether I'd like something or not. I tend to go for more serious plots and the art style can reflect that. I navigate through streaming providers' anime selection pretty easily. I could not have done that 10 years ago.
But yeah, series I remember blatantly putting my foot down like "NO, I WILL NOT WATCH YOU" would be Excel Saga and Chobits.
Excel Saga I just thought was so obnoxious and everyone was so obsessed with it and I just didn't get it. I don't like heavy humor most of the time.
Then Chobits I stopped watching because I'm a huge fan of the manga and I didn't feel like it was doing it justice. An entire episode dedicated to getting her panties? Really? emotion_donotwant
There have been PLENTY of anime that I have started and then just gave up on. crying
A couple of standouts include Black Butler, Mushi-shi, and Claymore.
Mushi-shi is a good anime, but I always started it up and then something would come up in my life and I wouldn't have time for it. Black Butler was kind of weird for me. Even though I found myself laughing sometimes, other times I was like "WTF." I got all the way through Claymore until there were only a couple of episodes left and I just lost interest.