It sounds like you are using semantics. A raw trade deficit is mathematically impossible, but you must know full well that when we use the term “trade deficity” it is conventionally accepted to mean a trade imbalance between nations.
So when we say the USA experienced a record “trade deficit” it simply means that the value of what we imported was at a record high against the value of what we exported.
I don’t know what phrase you would use for that concept, but it sounds to me like you are berating the use of a technically sloppy phrase rather than disagreeing with an economic concept.
In your 1st para, you say “trade deficit” is accepted to mean trade imbalance between nations.
In your 2nd para, you say the opposite.
Regardless... a trade balance between nations is possible, it happens, and it is meaningless.
An overall trade balance is impossible.