Well, a mystery it is. Let's review the situation -- it can be educational for others reading this, and it can help focus our thoughts.
When you end attacks, the drop down menu lists are populated. The "from" list is filled with those territories you hold which have more than one troop and a border through which you can reinforce -- that is, an attack route which leads to another territory that you hold. [We don't need to worry about different types of reinforcement, or team play, at least for now.] The list is sorted alphabetically, and the first item is selected. The "to" list is filled with the territories which can be reached from the selected "from" item, and again, the list is sorted and the first item is selected by default. If you select a different "to" item, it can only be another one reachable from that "from" item. However, if you choose a new "from" item, then the "to" list gets updated and things could go two ways. If the new "from" item can still reach the selected "to" item, then it should stay selected (and I believe it does). But if the new selected "from" item cannot reach (what was) the selected "to" item, then the selection must be shifted, and will end up on the first item in the updated "to" list.
I presume that your problem is not rooted in what I just mentioned. You said the "to" item changes as you move to click the "Reinforce" button. Do you have an ordinary mouse, or a touchpad, or what? Do you find that you are moving across the map area? Have you tried moving from the lists to the button by pressing the Tab key?
I just remembered that there can be odd interactions between the drop down lists and the clickable maps feature. Is it possible that you clicked with a middle or right button by accident?