The word "father" itself is grammatically correct. However, its usage in a sentence may be grammatically incorrect depending on the context.
For example:
* Correct: "My father is a doctor."
* Incorrect: "He is a father." (This sentence is grammatically correct, but it's unclear who "he" refers to. It lacks context.)
To determine if "father" is used correctly in a sentence, you need to consider the context and the grammatical rules of the sentence.