Big at the front should generally not be combined with big at the back, for two reasons.
It forces the chain to use a non-straight chain path, (hence "cross chaining")
The derailleur spring has to stretch out forwards to allow the chain to be mostly on the cogs.
You also want to avoid small front and small rear, for similar but opposite reasons.
The chain does the same out-of-line crosschaining, merely in the other direction
The derailer has so much extra chain to take up that it ends up folding completely up and the chain can rub on itself passing around the two jockey wheels. At extreme cases the chain can catch itself, and wrap itself around a jockey wheel. This tends to bring pedalling to an abrupt halt.
Chains wear out no matter what you do. Grit from roads, salt, and plain old usage wear a chain. You're recommended to fit a new one every 2000 km, but different brands have different numbers, plus your usage comes into it.
If you ignore the chain then it will slowly wear out the rear cassette, and then starts on the front chainrings. A $30 chain a year is cheaper than a new cassette and chain every two years.