If the point is to soft-pedal "committed suicide" or "killed himself," then the common phrasing is "take one's own life" (e.g., "My father took his own life.").
While calling your father "a suicide" isn't ungrammatical and doesn't definitively misuse the word "suicide" (see def. 3), it also isn't soft-pedaling it, which seems to be your aim, nor is it politically correct, much like how calling someone "a gay" or "a cripple" isn't politically correct. Pointing that out seems to be your literary agent's aim.
Calling someone "a gay," "a cripple," or "an anything" that is often highly charged with bigotry, judgment, or controversy is politically incorrect, is rude, the only exception being maybe if that person nominatively rather than adjectivally self-identifies as that. That's because when you call someone that thing, you are making that thing the person's identity, like that's what defines that person as a person, thus defining that person's personhood, which is especially true in this case since it represents a single deed, a single deed of your father's in an entire lifetime of deeds that perhaps shouldn't be overshadowed by it.
What your literary agent is doing isn't telling you it's ungrammatical for you to call your father "a suicide" or telling you you've misused the word "suicide" as it is defined in the dictionary. Rather, what your literary agent is doing is warning you off calling your father "a suicide" so that you don't expressly make "suicide" the defining act of your father's life, as if his suicide was all he was. Not only is calling your father "a suicide" politically incorrect at best and rude at worst, inaccurate since he was far more than that one act and deserves to be remembered for more than just that, and, most of all, unkind, but it's also hurtful towards yourself.
Words have weight because words, especially when repeated, convince, not just others but also ourselves. The words we choose influence, color, and codify our own feelings and opinions. By you calling your father "a suicide," you are chipping away at the identity — or the "personhood," as your literary agent put it — of your father in your own mind by dripping the poison into your own ear that a suicide, his suicide, is what he was, is all he was.
Now, police, hospital staff, mortuary personnel, etc. may in internal communications call your father "a suicide" to economize language by referring to your father as what about him is most salient in respect to the work they do, but even then, its appropriateness is debatable, which is why such organizations so often expressly advise employees not to use that terminology in external communications, like with family members, the press, etc. For a family member to call a loved one who committed suicide "a suicide" is unusual because family members, of all people, knew them and know "a suicide" is not who they were as a person but was just something they did in their final moments and generally want to remember them for who they were as a person in life and not for their suicide.