Is likening a human to an animal, such as "strong as a lion" or "like a falcon," forbidden, or does it have another meaning?

There is no harm in what you mentioned. Evidence for its permissibility is the Prophet's (peace be upon him) affirmation of Abu Bakr Al-Siddiq when he described Abu Qatadah (may Allah be pleased with him) saying: "A lion from the lions of Allah, fighting for Allah and His Messenger." The Messenger of Allah (peace be upon him) then said: "He spoke the truth."