A government can leave income tax rates unchanged and still take a growing share of someone's pay. Freeze the thresholds while wages rise and more income becomes taxable, or taxable at a higher rate. A pay rise that merely keeps up with prices can leave someone paying more tax without making them better off.
That is a tax increase people should be able to debate. Calling it a freeze doesn't change its effect.
Why governments use it
There is a defensible case for raising the revenue. Public services need funding, borrowing has costs and cutting spending has consequences. A threshold freeze is relatively straightforward to administer and can raise money over several years.
It is also politically convenient. Ministers can say they haven't raised the headline rates while the amount collected increases. The decision is public and has an author; it isn't literally a tax nobody voted on. The problem is that describing only the unchanged rate can conceal what the decision means for people's income.
A worker pushed into a higher band by an inflation-related pay rise may feel no richer than before. A pensioner can become liable as their pension rises against a fixed allowance. The effect varies with circumstances, which is another reason to explain it rather than hide behind the word "freeze".
Make the choice clear
It isn't enough to argue that a government has kept the letter of a promise about rates. Voters deserve to understand the expected change in what they will pay.
If the revenue is needed, explain why. Publish the effects of holding the thresholds still and defend them alongside the services or commitments they fund. Alternatively, uprate thresholds and argue openly for whatever further revenue is required.
No method of raising money will please everyone. That isn't a reason to make the choice harder to see. People should be asked to judge an increase as an increase, rather than assured that nothing changed because the percentage on the payslip stayed the same.