It appears that the confusion is arising over the first words “I’m sorry”.
Written words do not convey the emotion with which they are spoken. One can say I’m sorry…" in an aggressive, angry tone and the hearer does not here contrition, but anger. In this circumstance, “I’m sorry” may only mean “I’m sorry to unload on you but I have to tell someone - I am really angry about being coerced to go to…” The lead-in has nothing to do with confession; it is a semi-apology for bothering someone, not an apology for the anger.
On the other hand, one can say “I’m angry” in a low, contrite tone, and the hearer hears contrition, sadness, sorrow, (and etc.).
Neither the OP nor anyone else in this thread heard the individual who walked into the confessional (and according to the postings) started off with “I’m angry”, but the priest heard it. From the priest’s comments, it appears that he immediately perceived anger, not contrition.
Granted the fact that some people have not been to confession in a long time and may not know what is a fairly standard format for starting a confession (“Bless me, Father, for I ahve sinned. My last confession was XXXX ago and these are my sins:”), it is possible to start a confession by just getting directly to the matter - the sin(s).
But in doing so, most people who are intent in confessing sins are not going to come in and start in with an angry tone of voice, in a manner that is complaining rather than confessing.
In charity, we need to presume that a) the priest thoroughly understands the requirements of the seal of confession, and b) that he follows the the requirements of the seal.
The reaction of the priest, assuming a) and b) above, is that the individual who entered the confessional had no intent on confessing any sins real or perceived. It appears they were angry, and without being able to direct questions to them, we don’t know why they chose to vent at the priest. Perhaps they felt he was at fault for their feeling they were being compelled; it is not a stretch that they were somehow blaming the priest in part for their being present against their will (anger is not particularly logical in the objects it is expressed against).
As to the individual who addressed the priest, they may or may not have expected the matter to be under any seal; and given that many people do not understand the parameters of the seal that would not be surprising. Or the individual might not have even thought of the seal; they may just have presumed that if they expressed anger about something, the one to whom they expressed anger would not say anything no matter where or when the anger was expressed, or under what circumstances.
Or they may have never stopped to think about whether or not their comments would be confidential. They were just angry and venting. Emotions tend to trump logic, and anger is excellent at doing so.
The point that FrDavid96 is making is that most people who enter the confessional intend to start the sacrament of reconciliation. That does not mean that everyone who enters does so (my example of the the drunk applies). It is not a matter of “law”; it is a matter of intent.
One who intends to start the sacrament is given the seal by the Church, that the confessor may not reveal what was said (or not said - that is, they cannot reveal the substance of the confession). One who does not intend to start the sacrament (the drunk, or in this case, an angry individual coming in to spout off) does not start it and so there is nothing for the seal to attach to.
There is an entirely separate matter, and that is the issue of discretion. Discretion might indicate that something one person said to a priest should not be repeated to another, not because of any presumed privacy on the part of the one person, but simply because some things are best left unsaid. That one person may be telling others the same matter; they may even do it within the hearing of the priest, but discretion may be the wiser course even after it is clear that the speaker does not intend to keep things private.
As we know little about the conversation between the OP and the priest and have heard only one side, discretion within this thread would be appropriate; the priest is not available to defend themselves. That is not a statement about the OP in any way; just a suggestion that we not besmirch the priest’s character.
Would it have been better that he not have said what occurred? Maybe, but not having any opportunity to hear his side, we cannot actually judge that, only surmise. And that risks speaking for or against his reputation.