I really do not understand how to answer this question because i am not actually a muslim and i would love to understand. Could one argue that humans must not show mecy as Allah does because it is a God-like feature?
No. One could not argue that. This is an incorrect line of thinking because anything that isn't "God-like" is all that is evil and Satanic, which leads to Hell. Surely you understand that God does not want you to tread down that path.
Allah (ﷻ) wants us to show mercy and compassion to others as He said many times in His religion, so your confusion is just a matter of understanding His Mercy v. our mercy. Allah (ﷻ) has the Perfect Qualities; He Is Perfect in His Mercy and His Mercy is infinite. He is the Most Merciful. In contrast, we as humans are no where near as Merciful as He is nor are we perfect in our mercy. So we never could be Merciful exactly like Him. But we can be [and are expected to be] merciful as much/often as we can to a humanly extent. There is absolutely no comparison or likeness.