I understand why credit cards with embedded chips are more secure (since they generate one time codes), but why do they still have the magnetic strip? Is this for backward compatibility? Also, how does this affect the added security benefits provided by the chip? Can cards still be cloned as long as they have a magnetic strip, even if a chip is present, because of this?

Obviously some locations don't have chip-enabled terminals yet, so the embedded chip cannot be used for transactions everywhere. However, because of this, the card must still be able to be read via magnetic strip (and thus able to be copied, since all the magnetic strip does is provide the card information unencrypted, no?).