A simple demonstration in electrostatics can convince that London dispersion forces are attractive. Has your physics teacher shown "charging by induction"?
Charging by induction video
Now replace the rods by molecules. Note the rods always attract. If one molecule develops a dipole or negative charge (on one side), it will induce an oppositive dipole in its neighbour.
Second demo, which you should yourself. Open tap in such a way that only a thin stream of water is flowing, but not dripping. Charge a comb with your hair and bring it close to the water stream. You will see water is attracted to the comb. No matter what you use for charging, water always gets attracted. There is no repulsion, because the permanent dipole of water always orients itself in such a way that its end is opposite in sign to whatever is the charge on the comb.
Water attracted to a charged comb
Now van der Waals attraction is not due to permanent dipoles but transient dipoles.
BTW, atoms and molecules do repel each other if you try to bring them very close. Can you compress water easily? Why and why not?
P.S. Please don't consider the answers on the web as answers from the Heavens. Online answers are written by students, teachers, researchers, former chemists etc. and all of us can be right or wrong.