When singing a major scale, you do sing semitones, between 3>4 and 7>8. Must be done.
In the first 5 notes of a minor scale, only one is different from the major. The third. Surely you must be able to hear that it's different. It's the main reason that makes a tune minor rather than major. Concentrate on that difference and it'll help a lot. Listen to it in minor melodies.
If you can sing a major scale, then you must be able to at least sing a natural minor scale. Same notes, different root. Simply go up and down a major, and after a few times, add an extra note. Not C>C>C, but C>D>C, over one octave. Then C>E>C until you can climb back safely. Then do the opposite, C>C>B and if you need, back to C When you can start at A, and stop at A an octave higher, it's done.
Pretty much all we hear and sing is in major, so we're brainwashed to its sound. Listen for a week to only minor songs, sing only a five finger excercise in minor.
Don't get bogged down with melodic for a good while - use harmonic only.
When you do look at melodic, think there's only one note different from major going up - the 3rd - so that's hardly a tripping point, because by now, you've immersed yourself in natural minor, with the same lower 5 notes.
As much as anything, it could be fear of the unknown - 'this will be difficult, so I'd better struggle with it'.
Lastly, get used to singing a chromatic scale, starting anywhere in tessitura, and singing a few notes, along with an instrument.
Once you've done all this, it's a good time to visit modes, as that, to a degree, is what you've been singing. Your teacher will explain all that, and it's useful to any singer to be able to understand what they are and how they work.