I'm adding two lights to my restroom, why does the left switch have to be on before the other one works? How to make two switches independent

This is a problem of wrong wiring of the two switches, but your problem is not described clearly, I think it may be that when the left switch is turned on there is a light on, and then turn on the other switch the other light is also on, it is so.

The following picture shows: Figure 1 is the wiring schematic, the wrong wiring is so, switch two of the fire wire is connected from the switch after one;? Figure 2 is the wiring diagram of the back of the switch physical; Figure 3 is the correct wiring diagram after correction.