We experience high tides on two sides of the earth at once, the side which is closest and the side which is furthest away. The side which is closest is quite intuitive, the gravitational pull of the moon is strongest here, it exceeds the inertial force holding the water in place and so the water is pulled towards the moon.
The side furthest away is less intuitive. Apparently the matching tide here is because the moons gravitational pull is weakest here, inertia exceeds the gravitational force, causing the water to try and keep moving in a straight line, and so bulging out. (https://oceanservice.noaa.gov/education/tutorial_tides/tides03_gravity.html)
So why then are tides smaller at the equator? Turns out this isn't actually true, it's just true in some well known locations. See https://www.co-ops.nos.noaa.gov/faq2.html#27 and https://www.quora.com/Why-are-tides-lower-at-the-equator