Assuming you have a fairly recent version of MEP (it's always a good idea to give us this information in your post) you are almost certainly working in the "wrong" (for you) Mouse Mode.

See the picture I have attached - it's part of the left side of the tab above the Timeline, below the monitor/preview screen.  You need to ensure the first box is clicked, the one containing only an arrow.  this allows you to only deal with one object.  Almost certainly you have the second or third box highlighted (as the second is in my picture) which is the mode that automatically selects an object and everything on the same track to its right or, in the case of the third box, selects everything on every track to the right!

HTH

Jeff