Each of these is a refusal this regime lets a counterparty attempt, paired with the answer to it. Reading them before you write is worth more than any amount of polish on the letter itself.
"You agreed to the terms, which set out the renewal"
high likelihoodThe trader points at a terms page or a single acceptance checkbox at signup.
What answers it
Acceptance of general terms is not the same as informed consent to an automatic renewal, and in most of these jurisdictions the renewal term has to be presented clearly and close to the point of consent rather than behind a link. Ask the trader to produce the actual screen you were shown, with the date. If it produces today's checkout flow rather than the one in force when you signed up, say so.
Ley Federal de Protección al Consumidor, art. 56 — art. 56 — the consumer may revoke a contract concluded at home, by telephone, electronically or by any similar means within five working days, without liability
"Cancellation has to be done by telephone"
high likelihoodThe trader accepts online signups and insists on a phone call, a physical letter or an in-person visit to cancel.
What answers it
This jurisdiction regulates the exit as well as the entry. A trader that lets you subscribe in one click and requires a phone call to leave is not complying, and the mismatch between the two journeys is the whole of the complaint. Describe both journeys, in order, in your letter and in the regulator complaint.
Ley Federal de Protección al Consumidor, art. 56 — art. 56 — the consumer may revoke a contract concluded at home, by telephone, electronically or by any similar means within five working days, without liability
"You have to give a notice period, so the next charge stands"
medium likelihoodThe trader accepts the cancellation but insists on a further billing cycle under a notice clause buried in the terms.
What answers it
Ask for the clause, by number, and ask when and how it was brought to your attention. A notice period that was not clearly disclosed before you contracted is vulnerable as an unfair term in most of these jurisdictions, and a notice period longer than the billing cycle itself is vulnerable almost everywhere. Pay nothing pending the answer and revoke the payment authority.
"We are established abroad, so your consumer law does not apply"
medium likelihoodThe trader is incorporated elsewhere and says the contract is governed by the law of its own seat.
What answers it
A choice-of-law clause in a consumer contract does not usually deprive a consumer of the protection of the mandatory rules of the country they live in, and a trader that directs its activities at consumers in a country generally answers to that country's consumer regulator. Say where you live, say that you contracted from there, and copy the regulator named in this result. Meanwhile the payment route works regardless of governing law.