This is because removing such things is among the endless beauties of Islam which urges people to be clean, pure, well-conducted and well-educated. The ultimate aim of Islam is to make the Muslim be in the best state and the best image. No doubt that long nails that resemble lion’s claws are not beautiful.
Islam orders only that which is beautiful and prohibits only that which is ugly.
Not cutting one’s nails for more than forty days is dislikeable. Anas (R.A) said: “The Prophet (PBUH) fixed a deadline for us for cutting the nails, plucking out the armpit hair and shaving the pubic hair (he ordered us) not to leave any of those more than 40 days.”
[Ahmad, Abu Daawood and others]
From the above, as long as the nails do not hold any impurities and do not exceed a period of forty days (from having them), then there is no objection for leaving them. But after 40 days, they must be cut as specified earlier.
Allah knows best.