How did the Twin Towers not tip over

The structure got weakened immediately, then the heat basically was melting the structure. Then the building was unable to hold itself up, and collapsed on itself.
(Same thing for both buildings)

It may have happened differently if the plane hit close to the bottom, then it may have tipped over.
--A modern building is also designed to collapse on itself, to limit damage to surrounding buildings.

They were designed with concrete which is very heavy and with a deep foundation into the ground, usually hundreds of piles 50 to 100 feet deep. the weight and the deep foundation kept it from falling over after the impact from the plane.

The building was designed for wind loads which are much stronger at 1000 feet. Thus, the wind load on the building was very strong. This force was probably more than the impact of the plane.

To build a sky scrapper you start with a big hole in the ground. You then slot the tower into it.
A peg in a hole.

Science... new advances in science and technology improves our methods of construction and makes steel stronger and sturdier.

they were pure steel