Having an official bit of plastic that says the government is happy that the person pictured has the name on the card is not in itself harmful, and is useful when you do need to prove your ID, such as at the bank when you want to do something to your account that you'd prefer others not be allowed to do. If you've got a UK photo-ID driver's licence then you already have such an ID card. In the US, such things are officially recognised as ID, and it's possible to get a similar card to act as a state ID that is not a driver's licence.
The line is crossed when the bank, or other entity is required to report your use of that ID to a central tracking system, which is pretty much what the last UK attempt at ID cards was all about and why we all kicked up a stink about it. It's the difference between the ID card being a tool for you to use, and it being a tool for the state to keep track of everyone.
The problem arises that once the first one is introduced, where you have an ID card with no requirements imposed on carrying it or its use, it's easy for a future government to suddenly declare that you're supposed to carry it at all times, or introduce a reporting requirement on its use, or to require it to be presented for certain transaction types. Far easier to hold the line at "no government ID card" than give them that bit of ground and then hold back on the rest.