I can help explain a little better why skepticism has a bad rap among some: I turn to synonyms to get a ‘sense’ of the family of concepts it fits within common usage:
hesitation
disbelief
apprehension
uncertainty
reluctance
distrust
suspicion
indecision
questioning
faithlessness
dubiety
dubiousness
leeriness
agnosticism
lack of confidence
So even though you are using skeptic and skepticism as a technical term, the majority of the population, do not. This does not make you wrong by having fewer that could support your case, but it does explain its coloring and reputation for it is conceptually not a free and clear concept that stands alone. Defining a word with specificity when it is also used generally only convinces a few but not most. As a concept, it’s been long ago usurped to mean other things.