"For" can be a preposition, but only when it is followed by a noun or pronoun.
For example:
* For the dog: "For" is a preposition, and "the dog" is the object of the preposition.
* For you: "For" is a preposition, and "you" is the object of the preposition.
In the phrase "for a," there's no noun or pronoun following "for," making it incomplete.
Let me know if you have any other questions!