Should I tell my boss the real reason i am quitting?

So I am a 23 year old guy and i started my new job on June 1st of this year, as the Assistant Store Manager in a retail shoe store, i am the only guy in a store of 15-16 females. I have previous retail experience working in higher volume retailers, this store is only 3 million a year, other places i have worked have ranged from 20 million to 3 million in volume, also when i got hired the district manager sent me to a higher volume store to train for a week before I even set foot in my home store.

Long story short, the two stores and the two store managers are complete opposites. The store manager when I was training was very direct, efficient and ran a top notch store, in my home store the store manager is more about feelings rather than results, and numerous times she has stabbed employees in the back for her own benefit. in my short time there 5 people have quit 3 on the spot. my first 2 months i kept my mouth shut and listened to the store managers favorite employee who has been there 10 years, I made the mistake of speaking up and coming up with new ideas, and apparently I rubbed them the wrong way and apparently i was only hired on to play second fiddle to them, half the employees already said If i leave they have no reason to stick around.

So I have two job offers which i will decide on next week, but i am leaving already for a fact, should I tell my boss the real reason i am leaving or make up a fake B.S excuse.