Kirchhoff loop signs follow your traversal
The mistake
Changing voltage signs based on how a battery or resistor looks, not on the chosen loop direction.
Why it feels right
Battery symbols seem to carry their own plus/minus direction independent of your path.
How to catch it
The same element appears with different signs in two loops without a stated traversal rule.
The first principle
Pick a traversal direction. Across a resistor in the direction of current the change is −IR; across a battery from − to + the change is +ε.
You traverse a resistor opposite the assumed current. What voltage change do you write?
Common wrong move
−IR because resistors always drop voltage.
Correct
+IR for that traversal; the sign follows the path relative to current.
Make a fresh prediction before referring to the worked example.