Snape loved Lily. This caused his Patronus to take the form of hers.Lily's Patronus was a doe, and Snape knew this. Snape was in love with Lily and always has been and so adopted the doe patronus. Similar to how Harry's is a stag because of his father. It also probably has something to do with the memory Snape uses to cast the Patronus. Most likely the memory has something to do with Lily.Lily's Patronus was originally a doe. After she dies, Snape loves Lily so much that his Patronus changes to that. .
Edit: Might i add, snape was always loyal to lily
Edit 2: he didn't make choose to change his patronus, it changed on it's own because he did not realise how much he loved lily, and always kept a sense of denial about the whole thing, until his converstation with dumbledore, which 'always' mattered.