why we use "ing" with verb that comes after preposition?
For example: he is accused for breaking a new vase.
here breaking is being used after for
When a non-finite verb form is the object of a preposition, it is almost always a gerund, i.e., the present participle (or -ing) form of a verb used as a noun. The only reason we can give is that it's idiomatic in English, which is only a way of saying that's the way it is. Of course, this being English, there's an exception:
He was accused of breaking the new vase.
He had no choice except to defend himself.
The first sentence is the usual case: the gerund breaking appears as the object of the preposition of. The second sentence is the rarer case: the infinitive to defend appears as the object of the preposition except.