Light does go straight, but only from the point of view of what are called inertial observers (IOs). Standing still on the surface of the Earth doesn't make you an IO, but being in free fall does (approximately and, of course, temporarily).
So if someone was falling towards the earth, they would see nearby beams of light traveling along straight lines. But if you watched this from the ground, these beams look bent, in the same way the path of a stone through the air, which the falling person sees as moving in a straight line, appears to you to be bent (although the light bends to a much smaller degree due to its much higher speed). So that's how light can "look" bent, even though, in an important sense, you're right to say it never really bends.
Actually, because of the curvature of space, even IOs can see distant light bending, because the curvature means roughly that an IO at one point won't look like an IO to an IO in another location.
