There are plenty of good arguments against mandatory crypto backdoors. All of the ones I've seen invoke at least one of the following assumptions:

1. We can't trust the government(s) who want to hold the keys.
2. The government holding the keys can't keep their computer systems secure.
3. The government doesn't really need crypto backdoors.
4. The "bad guys" can write their own un-backdoored encryption tools and use those.
5. It's technically infeasible to backdoor a cryptosystem in a secure way.

Let's build an even stronger argument against mandated backdoors. We'll be insanely generous to the government and negate all of those assumptions. Assume the following:

1. The government is 100% trustworthy.
2. The government is capable of securing computer systems and protecting keys.
3. The government really needs crypto backdoors.
4. The "bad guys" will use U.S.-based commercial cryptography products.
5. It's possible to backdoor a cryptosystem in a way that's secure, but it's more difficult and expensive than if the system weren't backdoored.

Here's an argument against crypto backdoors that works even under these highly optimistic assumptions: Mandated crypto backdoors are like a tax on the use of cryptography, which incentivizes companies to produce less-secure products.

If we decide to obligate crypto backdoors then any company who uses cryptography in their products must be prepared to add the backdoor feature to their product. By assumption (5), doing so will incur an additional cost. The company must divert engineering resources away from other things – things that will likely bring the company more profit – towards adding the backdoor, which will bring the company no additional profit, since from the user's perspective it is the same. The company is therefore paying a tax, in the form of opportunity cost, to use encryption in their product.

In response to this tax, companies can compromise on security by deciding not to use encryption at all or by spending less engineering and quality assurance effort on the parts of their product that involve cryptography. This will make users more vulnerable. Or, they can choose not to compromise on security by very-carefully implementing the backdoor and accepting the loss in profits.

It's clear from the economic incentives that software written by companies mandated to add backdoors will tend to be less secure.

The true cost of mandatory backdoors is now in plain view. In order to circumvent my argument, the government (and by extension, the people) must be willing to reimburse software companies for the added cost to design, implement, review, and test the backdoor. This could amount to billions of dollars if the government wants backdoors in everything. That's money that could be spent on healthcare, disease research, and other things that actually save lives. Even if the government can convince us assumptions (1), (2), (3), (4), and (5) are true, and are fine with reimbursing the added cost, they still have to convince us that they can save more lives using the access those backdoors provide than we could save by spending that money elsewhere.