No, I don’t think the analogy works.

People have a freedom of who they associate with and do business with:

Boycott is when you decide not to spend your money someplace because you don’t agree with them. You’re exercising your freedom of association.

Cancellation is when a 3rd party demands that a employee/employer sever their relationship because the 3rd party disapproves of the employee. Here, a 3rd party is imposing on two other parties’ freedom of association.

Also, the substance of the speech is quite different:

- “You are wrong, and here are the reasons why” is debate.

- “You are wrong, and you should become unemployable” is cancellation. Cancellation is technically speech, but it is speech that is focused on imposing a high cost on other speech. Talk about the “paradox of intolerance” argument that the modern left loves to use.

Cancel culture is not boycotting. At least not what most people consider boycotting. Boycotting usually there's to not giving money to a company to try to get the company to change their ways (yes you could argue it is a way to try and cancel the company) cancel culture is trying to get someone fired, or get their event, contact, whatever cancelled. Because you don't like them. It isn't the same thing. Boycotting is telling people "please don't prize company x" while cancellation is going above that person and asking them to remove the person. Totally different concepts. And it is mean and nasty, it is basically giving someone a death sentence for something they may not have even done. And of course you have every right to ask for someone to be cancelled. But you should use that right judicially. And make sure the punishment fits the crime.

Cancel culture == swatting. Same thing, abusing the system to get what they see as justice. Heavy cancellation usually involves stretching the truth or outright lies; an employer is very likely to drop a (male) employee based on an anonymous sexual assault tip for example, even if it turns out to be unsubstantiated depending on how high profile the employee/business is sometimes they'd rather play it safe & fire them anyway.

As easy as it is for one of the many Indian scam centers to take your grandmothers money, it is just as easy for a wide-eyed innocent figure to tell you lies about someone and have you believe them. I don't think most people realise how many biases we all carry.