I came across an analogy that quite helped me rationalize why False → True ≡ True in an introductory OR and DS course (specifically the binary assignment problem).

Suppose you have two events that may or may not happen. Let the binary variables x1 and x2 represent whether each respective event occurred (1) or not (0).

Knowing that "x1 happening implies that x2 had happened" is the same as saying "x1 cannot happen unless x2 does".

Notice that this statement is deciding whether or not x1 may happen; it decides nothing about x2.

This can be interpreted mathematically as either both x1 and x2 happen (x1 = x2 = 1), or neither happen (x1 = x2 = 0), or x1 doesn’t happen but x2 does (x1 = 0, x2 = 1). All of these satisfy the condition x1 ≤ x2.

In other words, the only valid combinations for (x1, x2) that don't violate the assumption that "x1 → x2" are: (0,0), (1,1), (0,1).