Why can my Apple 5s receive short messages, but I can't send short messages on the mobile network, and I don't want to use imessage to send messages?

The root cause is that you can connect to Apple's server with wifi, but you can't connect to Apple's server with the carrier network. It may be the following situations: 1, the network signal of mobile operators is too poor, so you can try to open some websites with browsers and test the network speed with traffic; 2. The operator blocked the Apple server and deliberately made it impossible for you to use it. In the past, China Mobile did not reach an agreement with Apple. Both imessage and facetime were abnormal, and even activation was a problem. Now it is not; 3. If your system is jailbroken, there may be something wrong with some plug-ins.

Because I can't see your mobile phone, I can only recommend you a general solution. First restore the network settings, if not, restore the whole system.