Why can not I teleport after sending teleportation from the alliance but I have to pay diamonds?

Not sure I understand your situation. But the game has different types of teleportation depending o the situation, generally you have to have an advanced teleport to move to a specific location and these cost 2000 diamonds unless you have earned one as a reward from some of the events.

There is an alliance teleport that can be used one time only for the first alliance that you join. If you are sent one by your alliance then it can be used to move you close to the alliance leader. You cannot pick the spot.

If you tap on a spot on the map and choose to teleport there then you have to use an advanced teleport.

If this doesn't answer the question please reply with more details.