Why does Netflix take down movies and tv shows?

Well first of all legal reasons

But also, they put on loads of shows/movies each month therefore have to take some off, otherwise it would be a mess.

If you want to keep up to date with what shows will disappear in the following month or what news ones will come up, you can always google it. That's how I always do it

Maybe their is a time in which they have a contract with a specific show and when the contract is up they have to remove it from Netflix

the same reason a tv network stops airing a show they have syndicated to their network - contract expiration

sometimes renewal of contract isn't offered by the owner

They have to buy the rights to show them, they do not OWN the shows... they kind of RENT them.

Then after the contract is up, they can not show them legally. They would have to buy the right to show them again.

They rent the movies.