At the end of Philosopher's Stone, Dumbledore tells Harry that Snape was trying so hard to protect Harry because once James saved Snape's life.

He could have said the complete truth, something like:

Snape hates you because you look like your father, who was a bully that, together with Black, made Snape's life impossible and once almost killed him. However, Snape will make everything to protect you because he loved your mother.

Or, if that was supposed to be a secret, he could have said a white lie, only telling part of the truth:

Snape and your father didn't get along very well. But there is no way he would let any student die, if he can avoid it.

But why did he tell that lie?

At the end of Philosopher's Stone, Dumbledore tells Harry that Snape was trying so hard to protect Harry because James once saved Snape's life.

He could have said the complete truth, something like:

Snape hates you because you look like your father, who was a bully who, together with Black, made Snape's life impossible and once almost killed him. However, Snape will do anything to protect you because he loved your mother.

Or, if that was supposed to be a secret, he could have said a white lie, only telling part of the truth:

Snape and your father didn't get along very well. But there is no way he would let any student die, if he can avoid it.

But why did he tell that lie?