My response is that this could be a reference to the last day of the Church age or the last day when Jesus finally returns. Either way, you're ignoring the fact that there are two distinct events described in the Bible - one where Jesus returns with a shout and meets us in the clouds and another where he returns on a white horse with his armies.
Jesus Christ returns with the Angels in the final judgment, eternal kingdom
Verses 31-32, Jesus Returns with the angels, the final judgment takes place
Verse 34, The eternal kingdom is presented to the righteous.
Verse 41, The wicked are judged to the eternal lake of fire.
Verse 46, The righteous obtain eternal life, and enter the eternal kingdom in verse 34.
Matthew 25:31-46KJV
31 When the Son of man shall come in his glory, and all the holy angels with him, then shall he sit upon the throne of his glory:
32 And before him shall be gathered all nations: and he shall separate them one from another, as a shepherd divideth his sheep from the goats:
33 And he shall set the sheep on his right hand, but the goats on the left.
34 Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:
35 For I was an hungred, and ye gave me meat: I was thirsty, and ye gave me drink: I was a stranger, and ye took me in:
36 Naked, and ye clothed me: I was sick, and ye visited me: I was in prison, and ye came unto me.
37 Then shall the righteous answer him, saying, Lord, when saw we thee an hungred, and fed thee? or thirsty, and gave thee drink?
38 When saw we thee a stranger, and took thee in? or naked, and clothed thee?
39 Or when saw we thee sick, or in prison, and came unto thee?
40 And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me.
41 Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:
42 For I was an hungred, and ye gave me no meat: I was thirsty, and ye gave me no drink:
43 I was a stranger, and ye took me not in: naked, and ye clothed me not: sick, and in prison, and ye visited me not.
44 Then shall they also answer him, saying, Lord, when saw we thee an hungred, or athirst, or a stranger, or naked, or sick, or in prison, and did not minister unto thee?
45 Then shall he answer them, saying, Verily I say unto you, Inasmuch as ye did it not to one of the least of these, ye did it not to me.
46 And these shall go away into everlasting punishment: but the righteous into life eternal.