Why is this を and not に to indicate moving in a direction?
Unless this example is wrong? But it is from JapanesePod101
出る is not a normal motion verb.
means to participate in X.
For example, カタン大会に出る would mean to participate in a Settlers of Catan tournament.
means to leave a place. see Differences between 出るand 去る when expressing someone leaving
Because it is not moving "in" a direction. It is moving "from" somewhere, since I suppose someone is going out "from" the house.
In general 出る follows either を or から. There are cases in which you are actually referring to "going out towards some place/situation" in a more figurative way or with the meaning of "to participate" in which you can actually use "に". For example:旅に出る, or 社会へ出る, and others.
By the way, your example feels a bit weird to me, as I would rather say: 今日は天気が良いから、家を出る。I feel there is a missing connection between 良い and the next sentence 家を出る. Maybe even just changing to 良くて would be enough.
Anyway, you can find a detailed explanation on 出る here and some explanations and example on when to use を or から here (for example there is a difference whether you are talking of a concrete movement or not and so on).