How is Takfir permissible in Islam?

>Allah's Messenger (ﷺ) said, "Whoever prays like us and faces our Qibla and eats our slaughtered animals is a Muslim and is under Allah's and His Apostle's protection. So do not betray Allah by betraying those who are in His protection." (Bukhari 391) > Allah's Messenger (ﷺ) said, "If a man says to his brother, O Kafir (disbeliever)!' Then surely one of them is such (i.e., a Kafir). " (Bukhari 6103) > The Prophet (ﷺ) said (to us), " List the names of those people who have **announced that they are Muslims**." So, we listed one thousand and five hundred men. Then we wondered, "Should we be afraid (of infidels) although we are one thousand and five hundred in number?" No doubt, we witnessed ourselves being afflicted with such bad trials that one would have to offer the prayer alone in fear. Narrated Al-A`mash: "We (listed the Muslims and) found them five hundred." And Abu Muawiya said, "Between six hundred to seven hundred." (Bukhari 3060) These Ahadith clarify that anyone who claims to be a Muslim and offers Salah, faces the Qibla, and eats Halal food is a Muslim, and one who says such a person to be a disbeliever becomes one himself. So then how is it permissible to label Ahmadis (and other sects of Muslims) as disbelievers?