The only way it will look good is to cut the siding back so that it runs in to whatever you block out the corner with; perhaps a 1 1/2 x 1 1/2 trim piece. You could scribe it in but a little more diificult.

"We have an enclosed patio that we are trying to convert into a babies room..."

Remove siding, install interior finished wall up to brick.

Even if we removed the siding, how do we meet the drywall up with the brick?

Install an "L" bead (with integral paper tape) at the vertical edge of the drywall as close to the brick as practical and then fill the joint with a paintable sealant or a sealant the color of the brick.

I have read about L beads but don't understand exactly what they do for you, why can't you butt the bare drywall up against the brick?

"why can't you butt the bare drywall up against the brick?"

Brick is not that flat.
The mortar joints are typically tooled to be below the face of the brick.

A piece of wood helps hide the joint, and coupled with some caulk makes for a smoother transition.