If we are applying ourselves to the tradition that "major = happy" while "minor = sad", then here are the "reasons":
If two wavelengths of one sound line up with three wavelengths of another, the sounds are a fifth apart. If it's 3:4, it's a fourth. These sounds are still harmonious to us even though not as much as the octave sound. This is why they are 'perfect fifths' and 'perfect fourths'. 4:5 gives us a major third, 5:6 gives us a minor third, 6:7 gives us something between a minor third and a major second (which we usually approximate to a minor third) and 7:8 does the same (which we usually approximate to a major second). Beyond that the intervals are no longer really harmonious enough for our ears to pick them up, and they just sound clashy. So because a minor third is more clashy than a major third, we perceive it as a little more off and this can translate into sad. [source: reddit]
Furthermore, the harmonic ratios of a major triad is 4:5:6, while 10:12:15 is for a minor triad. In a major key, the tonic triad is a major triad, while in a minor key, the tonic triad is minor.
Therefore, during the old days, it was interpreted as major keys were "happy", while minor keys were "sad." However, this has been rendered obsolete; therefore, this is rather based on people's opinions today, and are in fact not universal at all.