Why I am jewish but still have to proove it going throughout conversion?

I’ve learn that my mom isn’t jew, (she learn it the hard way, her mom didnt convert she had no idea). So basically, I’m jew, but since my granny didnt convert, I’m not recognized as one officially. Its a bit unfair since i grew up going to the Syna, did talmud, my parents and grand parents are a part of the community. I grew up in more faith than some jew who have their Judaism just past down to them and consider it as a annoying things to deal with. Anyway, I’m a bit upset, I’m going tru the process of conversion because i don’t want to feel the negative emotion that my mom have to deal with. (being jew but being not consider as one by the Beth Din) So yes, I’m so upset, plus I’m a progressist, and the Beth Din in France is not. They try to do everything to discourage you to convert. Which is so fucked up for ppl in my situation. Grewing up in faith and having a part of our identity taken away, and being judge by our own community. (plus the rabbin of my childhood left to Israel, so the new one is not progressist and you can feel (me and my mom) not welcome anymore. Even so we have always been a part of the community. Kinda fed up to feel judge, and don’t want to go to the syna because i don’t like the rabbin. (the member of the syna now are.. No kissing on the cheek btw male and female (french here) and they put a veil btw man and woman section. And man start to be ignoring woman. We are a very small community, so its odd to see cousins and others distance themself like that. So I’m sorry to complain, but i will have to go through that, and I’m afraid to become an extremist like them. (my dad agree that they become extremist, my mom find it great to go deeper in belief and practice) I needed to vant since i cant complain to nobody (my parents dont know i try to convert, it’s a surprise if I’m able to finish the process)