As I understand from your description, you use loop cut tool from toolbar:

[![enter image description here][1]][1]

So then you press to make a cut, not release mouse button, instead move cursor to the sides, and you will see that you are able to slide loop cut to the sides. Release button only then you like the position of the cut.

If you press <kbd>E</kbd> while holding the mouse button, you will see that the loop cut is parallel to one side. If that side is wrong, press  <kbd>F</kbd> to flip the side.


[![enter image description here][3]][3]

Also, you can use knife tool which give more freedom in making cuts

[![enter image description here][2]][2]




  [1]: https://i.sstatic.net/Fv99o.png
  [2]: https://i.sstatic.net/wcJPr.png
  [3]: https://i.sstatic.net/Vlkuw.png