Bringing up a grid from scratch from a total blackout scenario is such a time consuming process so you rather throw consumers off with no warning even in the coldest winter imaginable.
The problem was they could not import power from the Western grid (little interconnect capability for political reasons) and meanwhile El Paso and some border counties is humming right along because they are tied to the Western grid and not ERCOT.
In most houses you have a fuse box or breaker panel, this is to prevent the appliances from drawing too much current. Conductors heat up according to their resistance and the current applied to them, so if a circuit with 14 gauge wires suddenly has a load of 2000 watts applied to it, it will begin to heat up. If this load is applied for too long it can get hot enough to start a fire inside the walls of a house. This is why we have breakers - they will cut the circuit if it exceeds a safe level for too long.
Power grids don't really have breakers. They have complex control systems and highly trained operators to serve the same purpose. If transmission lines have too much current applied to them they can expand and sag, catching on other wires or structures causing damage and outages. Overloads can also damage substations and transformers for similar reasons (heat, thermal expansion). In this case, they did exactly what they had to. They cut the power to millions of people for a few days and saved their infrastructure from months of repairs if things went catastrophically wrong.
However, the total amount of power would remain the same, which means that the electrical current would increase to compensate.
The problem is that the amount of current increase is a square law increase compared to the voltage,
V = I * R
P = V * I
P = I^2 * R
So now you have equipment having to deal with the heat created by resistance (since nothing is 100% efficient), but way more heat than it can handle.
I'm not an electrician either, and my knowledge of AC isn't great, so I'm sure there are other reasons too, like the frequency is also effected if the generator can't keep up with the load, and that causes other problems
As they reach their capacity they start to droop quite a bit, which in itself can cause issues like touching something they usually would not.
Because HV lines are made from aluminum they loose some of their strength as they are heated up. Above 100C or so the aluminum anneals which means strength is lost. Now you just need some wind shaking those lines and the whole thing breaks. If you have reached that point you likely have to replace the entire length of the HV line.
Of course the cold weather counters some of this. But only to a certain point.
If just one HV line fails you now have to deal with the cascading effect as the current is load balanced on the remaining HV lines.