When you try to switch a (bipolar -- NPN or PNP) transistor fast, there are some effects that limit the rate it can respond.
1) The physical base of the transistor extends over some (small) area, and the base lead is only connected to one portion of this. There is some internal resistance between the connection location and the most remote portions of the base. When you switch fast, the time for the charges at the remote portions to be extracted is significant and limits how fast it can turn off. This isn't as severe for turning on because you could get by (for a few ns) with just the local portion turning on.
2) There is a significant capacitance between the collector and base. When turning off, the collector voltage rises (if it didn't there would be no need to turn the transistor off). This couples via the base-collector capacitance and tends to counter the turn-off or -on voltage on the base, thereby making it harder to turn on or off.
3) It actually takes some time for the carriers to transition the base and collector regions.
However, bipolar transistors can be very fast -- they can be switched in picoseconds inside ICs. Discrete devices can't be switched as fast because of greater parasitic capacitances, inductance of the wires that attach to the device, and because the fastest devices have breakdowns of just 1 or 2 V, and so are really only useful inside specialized circuits in ICs.