You as the author of an answer can delete your answer at any point. Apart from that, your answer can only directly be deleted by a moderator, should they find (possible through flagging by other users) that your answer is not really an answer, or through voting by 3 users with a reputation >20k, should your answer be negatively scored.
The other option is for your answer to be "deleted" as part of the deletion of a question. Again, moderation can be at play here, but the OP of a question can also still delete his question should none of the answers have reached a positive score.
There isn't really a defence against answer deletion as such, apart from contributing a good answer which receives upvotes.
At no point do you have to delete your answer because anyone asks you to do so. This is entirely up to you. Should you have been pressured into deleting your answer then this is inappropriate. If persistently pressured into deleting it, a flag for moderator attention might be appropriate.