"Opportunities of" vs "opportunities for;" which one is correct and why?

Solution 1:

As an American in California I would only use "for" and would find it completely strange to use "of".

In American English an "Opportunity For" Something, is always the object being given: I was privileged with an Opportunity for improvement, I was privileged with an opportunity for self-employment.

You could also have "opportunity to": I was privileged with the opportunity to go home, I was privileged with the opportunity to take the lead"

You may have been thinking of this due to some examples where "of" indicates a more exact meaning of the preceding noun. Like "I was privileged with the power" vs "I was privileged with the power of healing", the second sentence being more precise.

In general and in my experience "Of", being used like this, would be used to indicate that the preceding noun 'belongs to' the noun following "OF" as a form of describing the preceding noun (in a metaphorical sense); As in, "Place OF Interest" (a place that is interesting), "Flights OF Fancy" (a flight that is fanciful), "Feats OF Strength" (a feat requiring strength), "Birds OF a Feather" (an english idiom where the Birds share the same feathers/attributes) , "The Sound OF a horse neighing" (the sound a horse makes when neighing), "Color OF Love" (the color that best describes the feeling of love), "Power OF One" (how powerful one is). Therefore "Opportunities of One-on-One interactions" makes it sound like the "opportunities" were being given by the "One-on-One interactions" rather than "the interactions" being the "Opportunity" itself, as is your intention.

That is to say: your sentence doesn't make sense with "of" use "for", but if you had "opportunities of interactions" you would be thinking about the opportunities the interactions would be giving you, not that the interactions were themselves an opportunity. So "of" in this case provides that the preceding noun is an attribute of the following noun. The opportunities are a result of the interactions.