Think of the probability you assign as a measure of how "not surprised" you would be at seeing a certain outcome.

Total probability of all mutually exclusive possibilities has to add up to 1, right?

So if you would be equally surprised at heads or tails coming up, and you consider all other possibilities to be negligible (Or you state your prediction in terms of "given that the coin lands such that one face is clearly the 'face up' face....") then you ought assign a probability of 1/2 to each. (Again, slightly less to account for various "out of bounds" options, but in the abstract, considered on its own, 1/2)

ie, the same probability ought be assigned to each, since you'd be (reasonably) equally surprised at each outcome. So if the two have to also sum to 1 (100%), then 1/2 (50%) is the correct amount of belief to assign.