You have been mislead by the banks. They want you to believe that chip transactions are safe. The problem is the mag strips still exists and the chip usually contains a full, unencrypted copy of the mag stripe data. You can test this yourself by buying a programmable or USB chip reader.
The chip does have the capacity to have a card without stripe and even fully encrypt its data and even do simple crypto on chip but to date, many merchant banks (even big ones like Walmart) do not work with an encrypted chip.
IF the chip even does anything useful, the only data that is safe is what is on the wires between the chip reader and the bank. Chips could have easily been replaced by requiring strong TLS encryption and a custom key in the mag stripe.
Additionally, by the time the chip was declared ready to be used (a decade ago) the (homegrown) crypto was already outdated and researchers published papers on how an attack could be executed because those little chips don't have the compute power for anything better, it reuses keys generated with a very poor PRNG. By now, it is feasible to clone encrypted chips and force it to do weak, crackable crypto (with a bit of time on a decent computer). Once banks get around to go chip-only (another decade or even 2), I think it will be feasible to put the entire hack into one of those skimmers.