you do make a good point about the actual cost of building property (btw the difference is the price of land), however dont deny its a subsidy. if the state is providing support to offer a price below market rate, that is by definition a subsidy. you are also saying it should be a right, if one can choose to turn up to the council and ask for a home, thats infering a universal right to housing (rather than a welfare provision for those unable to support themselves)
I view it differently. Offering something below market value isn't subsidy as its money you don't have. If a mate in a bar can afford to sell me a pint for £4 or £5 but decides to sell to me at the lower price then the £4 pint isn't subsidised....its just a £4 pint. If he can't afford to sell me the £4 pint that's subsidy as its costing him sunk money.