Why did snape have a doe like Emily?

Snape did not have a doe-like Emily as a love interest. You seem to be mixing up characters from different works of fiction.

* Severus Snape: A character from the Harry Potter series, his love interest was Lily Evans, not Emily. Lily had red hair, not brown like a doe.

* Emily: This name is common, but it's not associated with any known love interests of Snape or any known doe-like characters in Harry Potter.

It's possible you're thinking of a different story, perhaps a fanfiction or a different book entirely.

Could you please clarify what you're referring to?