Emotions, especially strong ones, tend not to be based in conscious reasoning.
And even if they originated from conscious reasoning, that doesn't mean the degree of the eventual end result of the emotions experienced is justified by that reasoning (e.g. one's reasoning may justify some mild concern, whereas what one experiences may be total panic).
Fear specifically is a good example, because there are plenty of irrational fears out there (see, for example, a list of phobias, which may include more and less reasonable fears). Fear can also be crippling or make you freeze up, which usually isn't a very helpful or consciously-desirable response, and for some people it can take years of therapy to deal with their fear to a sufficient extent to be able to productively function in society. This is not what one would expect if fear was driven by reason.
If you are averse to something due to reason, this would not typically be "fear", as such. Most people don't "fear" cars, but they nonetheless realise that it wouldn't be the best idea to step into traffic. Although there is also a more primal fear response that may trigger when one is actually in front of or near a fast-moving object.
If a pedestrian suddenly and unexpectedly finds themselves in the middle of a road, this is where the causal line behind emotion may begin to blur. On a conscious level, you may realise this is where the cars go, and that may trigger a fear response. Or one might have a subconscious association between roads and fast-moving giant metal boxes, which can trigger a fear response without having to involve reason.
Realising that one's beliefs contradict other information one receives (i.e. cognitive dissonance) is arguably an example of emotion originating purely from reason.
Side note: this may be more of a psychology question than a philosophy one. A related question that could fit into either domain is the degree to which emotion biases reason (and it does, to a significant degree).