When you infringe on someone's space, time, or rights, you're getting involved in a way that is not cool. That's why, when you violate a copyright, you're said to infringe upon it.

Infringe is almost always used with the prepositions "on" or "upon," as in, "if you infringe on my rights, I'll sue you." Nobody knows why that's the case. Our language is full of rules and traditions that just are the way they are. We call these phrases "idiomatic." To infringe "on" or "upon" something is one of those. You don't infringe "into" someone's conversation. You infringe "upon" it. Case closed.

Definitions of infringe
  1. verb
    advance beyond the usual limit
    synonyms: encroach, impinge
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    type of:
    advance, go on, march on, move on, pass on, progress
    move forward, also in the metaphorical sense
  2. verb
    go against, as of rules and laws
    synonyms: conflict, contravene, run afoul
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    type of:
    breach, break, go against, infract, offend, transgress, violate
    act in disregard of laws, rules, contracts, or promises
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