How to correctly use 恐怕
As a native Chinese speaker, I would say "恐怕" is used most frequently in the context where the speaker expresses his belief that something he does not wish to happen might happen. For example, the coach of L.A. Lakers may say "恐怕 Kobe 不能再打籃球了", i.e. "I am afraid Kobe will not be able to play basketball anymore". 

Nevertheless, like in English, "恐怕" sometimes can be used to express conceding attitude. For instance, we may say "恐怕你在這點上是錯的", i.e. "I am afraid you are wrong in this point".