If you read what I wrote I didn't claim you said that price would increase. Since it isn't necessarily true that the price of education would increase given more subsidies for it then one should argue that this is likely to be the case in this instance. Indeed, it seems unlikely to be so to me because it's easy to limit the demand.
I didn't make this claim. Let me repeat: "...if you subsidize something more, you are likely to increase demand for it and raise prices further..."