Although in modern use learning against a wall or similar constructions have become akin to a new word, with slightly different meaning than to be opposed or against something. They are actually not two almost separate words. learning + against simply means it the wall was not there acting opposing 'gravity' the bike or the person or animal 'leaning against' the wall would fall down. It is a kind of reverse logic. = not that the wall is actually physically pushing against the bike, person or animal, but the bike, person animal is using the wall to oppose [be against] them falling down; because of the way they are leaning with gravity and the centre of balance acting against them. 'leaning against the wall'. One word many uses and in modern times, that phrase "leaning against the wall" is like a negative question except it is not a negative question but a positive statement. You, they, the man, bike, object, animal is leaning and up against the wall.
The argument holds true in all senses of the word. You would have difficulty remaining standing if you were not 'leaning - beginning to fall and (up) against the wall". If the wall were not acting against your precarious leaning stance, you would be in trouble.
The dictionary definitions of touching are just to attempt to give a simple explanation for modern usage for a very ancient word always with many uses 'again+st".
NOTE:
in modern usage you always 'lean a bike or object against a wall/door" etc to prevent it falling down. You always lean against a wall/door or table etc, to give yourself support, either to prevent falling down or to have a sort of half rest when tired,