I was thinking if F1 score is usually correlated with support in classification problems. In theory, shouldn't the F1 score increase for a label if there is more support? Why does this not always happen?
The support only relates to the ground truth. It is the same whathever your result is. On the contrary, the F1-score is computed from your actual scores thus depends from your results.
Thus, there is no direct link between support and F1-score in theory.
You can have an indirect link if the model performs better on a particular class. In that case, the more sample in that class, the larger the support and the higher the F1-score. But it is really due to the fact that
the model performs well on that class thus the F1-score increases
the class is larger thus the support is larger