Why are tea molecules moving out of the tea bag and into the water?

I think the answer is diffusion.  In diffusion molecules go from areas of higher concentration to areas of lower concentration.  When you put a tea bag into the water the tea bag has a large concentration while the water around it has a very low concentration.  Due to the concentration difference the tea molecules will leave the tea bag (area of high concentration) and move into the water (area of low concentration).  The tea will continue to leave the bag until the concentration in the water is equal to the concentration in the bag at which the rate at which tea laves the bag will be equal to the rate at which tea enters the bag.   At that point the system is said to be in dynamic equilibrium since the molecules are still moving around but due to the fact that the amount of tea entering and leaving the bag is the same there is no net change that we can see.

Diffusion works in this case since both the water molecules and tea molecules can pass through the bag freely.  If only water could pass through the bag freely you would have a hypotonic solution where water would be entering the bag trying to equal the outside and inside concentrations.  This is an example of osmosis and the result of that would be that the tea bag would bloat up as water rushed in it.

I hope this helps.  Let me know if you have any further questions or need anything to be clarified.

Solubility would be your answer.