As simkin says, don't take the posting as gospel - mainly because his (?) view is incorrect.
The M1 visa is transferrable to any other M1 approved school.
Ask the "old" school to put you on the "transfer" list, then ask the new school to pick you up as a "transfer student".
It's quite possible that, due to the cat fight nature of the aviation industry, the old school will not want you to move away to their competitor and may either say that transfers are impossible or they may simply refuse to do it.
If this happens, move to the new school and get the SEVIS telephone number from them (the old school probably will not give it to you), then YOU - not the school - has to call SEVIS and ask for the transfer. They will do it for you.
If you just change schools without doing the electronic (computer) transfer or calling SEVIS then you would be in breach of your visa and bad things could happen if anybody found out.
M1 transfers are fairly common - but you have to do it right.