Why does "Do you read me?" mean "Do you hear me?"
This phrase is used (in movies) during radio communication, for example.
The use of the word "read" in spoken radio transmissions was used to ask "how well is my message being received"
When using electronic voice communication, it is useful to know the quality of the signal being received. So the question "how (well) do you read (my transmission)" is asking for an indication of quality. The speaker wants to know if he needs to speak slower or louder to insure the message is received.
This is all part of voice procedure
A typical response might be "I read you 5 by 5" where the first number indicates the strength of the signal on a scale of 1 to 5 and the second number indicates the quality of the signal (how much noise there is).
"I read you five by five" means "I read you loud and clear" which implies "I hear and can understand everything you are saying"
Besides its most popular meaning, read also means "to understand" or "to interpret". Consider the following examples:
In radio (especially two-way) and telecommunication, words like roger, read and copy are used to clarify that communication has actually taken place. In potentially critical situations, the sender must always confirm their message has actually been understood and not just heard or read (in a literal sense). Examples:
Several agencies and professions (e.g. aviation) have developed their distinct vocabulary for confirming the receipt and understanding of communicated messages.
It isn't "hear me," since it means "hear and understand the words of (someone speaking on a radio transmitter)."