You usually purchase an admission ticket without being coerced to do so. Tax forms are filled with threats about what will happen if you do not comply. So while "punish" may not be the right term, it isn't anything like an admission ticket.
Your sentences are textbook examples of equivocating.
>People use the term punish when they feel like they've been punished.
Yes, they often do! Notice the word you just used to describe Shinkei's post? You wrote "feel" to describe "punish-as-in-sentiment-figure-of-speech". It's feelings/sentiments/perceptions etc.
Your attempted explanation after that was this:
>you're only punished if you fail to pay.
This is "you're only punished-as-in-assets-seized-or-go-to-jail if you evade taxes". It's a switch in semantics.
Because punish-as-in-sentiment is not equal in meaning to punish-as-in-jail, your proposed clarification is a non sequitur.
Since you're not aware of why one type of meaning (feelings) is not relevant to the other (jail), you are equivocating.
>I'm trying to figure out why people immediately think they are being punished by taxation somehow completely forgetting the [government services]
I know and it's understandable that you want to satisfy a curiosity. However, you'll just annoy people if you're equivocating 2 different meanings to justify your perspective while asking your question.
If someone says they feel "raped" by high taxes, you don't ape MrSpock and say "I see no genitals forcefully entering any orifice so I don't understand why people call it rape."
>they are an admission ticket to society.
They are not an "admission ticket". Admission tickets are pieces of paper that you submit to an usher or gate agent to be admitted to an event or airplane. (If you find that dissecting-figures-of-speech with literal definitions to be annoying, you've experienced firsthand why equivocation derails the discussion and is not helpful.)
Lastly, it seems like your answer to Shinkei was based on thinking he was against all taxes. If you read his post again, he was playing devil's-advocate for paying "punishment" taxes on a yacht. It's entirely reasonable for that type of person to raise taxes on himself for more police officers but feel punished for extra consumption taxes on luxury items since he's already paying sales tax on it.
I'm not saying he attacked Shinkei. couchand criticized the message and not the messenger which is certainly acceptable. I'm pointing out that he's criticizing a figure-of-speech by stating to us the legal literal definition of "punish". Because couchand didn't parse Shinkei's "punish-as-in-sentiment", he made the mistake of equivocation[1] and talks about punishement-as-in-prison-sentence-from-illegal-tax-evasion.
It's as if someone says "butterflies in my stomach" and a nitpicker adds a ST-MrSpock/ST:TNG-Data type of literal reply. Mr Spock asks, "Why do people use the term 'butterflies'? Caterpillars cannot incubate in the human stomach and metamorphose into a butterflies." Most observers would find that response annoying instead of being relevant to the conversation about nervousness.
Sure, there can be other motives such as helping someone conquer stage fright but hopefully you agree that correcting someone with formal biology definitions of "butterflies" does not achieve that objective at all.
[1]http://en.wikipedia.org/wiki/Equivocation