Why does riding the same motorcycle curve faster require a larger lean angle?

Answer: Because the same radius needs a larger inward acceleration

Because the tires need more spare grip before they slide — Grip decides whether the tires can supply the needed sideways force without sliding, but it is not the reason the lean angle rises. On the same curve, the required inward acceleration grows as speed increases. More grip only gives the bike enough margin to meet that demand.

Because the rider feels a stronger outward pull from the curve — The rider may feel thrown outward, but that feeling is not a new force pulling the motorcycle away from the curve. In the road frame, the tires must push the bike inward harder as speed rises. The lean angle grows to balance that larger inward requirement.

Because the same radius needs a larger inward acceleration ✓ — For the same curve radius, the needed inward acceleration grows with the square of speed. A motorcycle leans so the tire force and gravity line up with that acceleration demand instead of tipping the bike over. That is why a familiar bend can need much more lean when taken faster.