Is my teacher wrong?

Teacher: why weren't you in school 

Me: my stomach was hurting so I stayed home

Teacher: prove your stomach hurt

Me: That's impossible because there's no way to prove my stomach hurt, besides me saying that my stomach hurt

Teacher: so then you were skipping, if you can't prove your pain

Hi, Whimsicott!

I hope I can add help to your situation. Request your school to provide their policy’s definition of “truancy”. This is a start to determining whether your teacher is wrong. The policy handbooks for the two major high schools in my town have their policy handbooks published on the internet for free. Check yours. At these schools, illness is an excuse for absence. For all we know, your stomach hurt on account of an illness.

If the policy above generally holds across schools, your teacher is wrong in so many ways that you may need to talk to your principle about her conduct in order to avoid future problems from her. She states:

“so then you were skipping, if you can't prove your pain”

Notice the “so”. That means that the statement is a conclusion. This is how we know that she has given an argument. How do we know what her argument is if all we have from her mouth is the conclusion? We know what her argument is because she is drawing upon things that you said. Putting together your thoughts and her thoughts will produce the whole of her argument. You said it is impossible to prove our pain. That is what her conclusion is drawing upon. Her argument is this:

1. If you can’t prove your pain, then you were skipping
2. You can’t prove your pain (what you said)
3. Therefore, you were skipping. 

The conclusion follows—she has accomplished that much. Your teacher irresponsibly does not define what counts as proof. You did not either, but she introduced the word into the conversation and so should have defined it for your sake. If she means provide a doctors note, then premise 1 is false. Confirmation of your bad health from your parents or guardians is not a doctors note but does validate an absence. If by “proof” she means either provide a doctors note or confirmation from your parents or guardians, then premise 2 is false because you can prove your illness through the witness of your parents or guardians (here, I am assuming that your parents or guardians know you were in bad health.) If by “proof” she means basically a philosophical argument, she is deviating from school policy. By the way, contacting your guardians is the school’s responsibility, not yours.

Have the school contact your guardians. Request the school’s policy on truancy for future reference and perhaps tell the principal that teachers should speak clearly towards their students on what the policy is, instead of asking students ambiguously for “proof.” 

From, Kaiden

argument from ignorance 

Absence of evidence is not evidence of absence.

The wording here is slippery. The setup uses the word "proof" as a substitute for "evidence." It is evidence that substantiates the proof. The only evidence is the testimony of the student: "my stomach hurt." At that point, the burden of proof shifts from the student to the teacher to show whether the proffered evidence is true or false. 

The Fallacy of Equivocation is the misleading use of a term with more than one meaning, usually accomplished by glossing over the meaning initially intended in the discussion. Restated: it is to change the definition of a word within the discussion. BTW, often, this is a technique commonly in concert with moving the goal posts. 

"If you can't prove your stomach hurt, then you were skipping class."

Sounds like a non sequitur to me. You can't, strictly, infer that because someone can't prove their stomach pain that they weren't actually in pain, and were thus skiving off school. This is because a dishonest student couldn't prove their pain, since there wasn't any, but an honest student couldn't prove their pain either.

"prove your stomach hurt"

Your response, "f*'ck off. You're my parents employee"

Problematic language aside (prove), the teacher is asking the student to support his claim when contributory evidence beyond the anecdotal is unavailable, and may reasonably be seen as unreasonable or impossible. When this arises in a legal context it is dubbed “probatio diabolica (Latin: "devil's proof", "diabolical proof"). Remedies in that arena often utilize a reversing of the burden of proof, or giving additional rights to the individual facing the probatio diabolica.

Aside from this appeal to the impossible or unreasonable, the teacher is also engaging in problematic polysematic language (prove) and a non-sequitur (if not x then y.) 

argument from incredulity

Non sequitur and argument from ignorance