One of my friends told me that "will be able to" is a wrong phrase. Able doesn't fit with will. Is this true?
He has it backwards. The modal verb can, which means the same thing as to be able to, cannot be put into the future. If you want to say that modern medicine has the ability to cure cancer, you could say:
We can cure cancer.
We are able to cure cancer.
If you want to say that modern medicine will have the ability to cure cancer in the future, even if it currently doesn't, you don't say
*We will can cure cancer.
but instead, you say
We will be able to cure cancer.
Will is used to express the future tense of a verb; "I will be able to" is simply the future tense of "I am able to."
Modal verbs such as might, may, can, or should are not used together will.
This is obviously not true. The reason being, there's no reason not to use them together... they don't even contradict one another. (Not like something "He might run for certain". That's certainly wrong)
"able" denotes the ability to do something.
"Will" denotes that something is going to happen most probably.
Thus, using them together, it means "someone has an ability to do something, and is going to use that ability in near future".