Very Basic Electronics Question regarding current flow
I believe the secret is in the transistors. The current on the right half is flowing straight to ground because of Q2. Q2 is active because of the small current to its base, the vertical line, from the left side.

The next question is why Q1 doesn't get activated like Q2. What prevents this is the 1K resistors. Once the current is past the 100 resistor on the left side, the only place to go is into Q2's base. On the right side, because of the 1K resistor, most will just run to ground and Q1 is never tripped.

When you press the Set switch, Q1 is switched on by applying current to its base and the reverse happens. Current on the right is now diverted to keeping Q1 open and current on the left runs straight to ground.