Your garage door controller wall station has learned your neighbor's transmitter (remote opener) code. This problem has happened to me and several of my neighbors over the years. We all have the MVP Allstar garage door opener systems which is widely used in The Villages. There's a procedure for erasing the codes currently stored in the wall station's memory and then re-learning ONLY your remote's code. Here's a link to the Manual for this unit.
http://www.linearcorp.com/pdf/manuals/111069FX1.pdf
Page 12 has the instructions for erasing and re-learning transmitter codes. You'll also need to re-program your Wireless Keyless Entry keypad. Here's a link to the manual for doing that.
http://www.linearcorp.com/pdf/manuals/111214B.pdf