Severus Snape is not old, and he is not young. He is at the age where people see him as a confirmed bachelor. Severus is a man who never had want or need of a wife or a flock of children, it seems. He has a general dislike for children, and he doesn't seem the type who believes in concepts as romantic as true love.
But, the way things seem and they way things really are rarely are one and the same.
It's true, Snape is not a romantic. There is no poet's soul under his sneer. In many ways, Severus Snape is exactly the man everyone thinks he is.
And in so many others, he is not.
Snape had a wife. There was no ceremony, no celebration, but he vowed to love only Lily Evans until the day he died, and so he has. It doesn't matter that she called James Potter 'husband' and not Severus. What matters is the depth of his love and the unwavering conviction in the vow he made.
And so, because Snape had a wife, (has a wife), Snape also has a son.
His son's name is Harry Potter.
Snape loves his son, because he is Lily's boy. Snape hates Harry, because he is James's child. At the end of the day, the love for his wife is greater than the hatred Snape has for the man Lily married. At the end of the day, he loves Harry Potter.
And now, at the end of his life, as his last few seconds are approaching him, Snape is glad his son is here with him, looking at him with his wife's eyes.
"Look. At. Me," he tells Harry, and it's the closest he will ever get to saying, I love you.
His epitaph will not read 'husband & father' because he has never been either of those. What he is is simply a man who loved his wife and protected his son, even though they were never his.