Please note that this verse does not say that one day is a thousand years. It says that, with the Lord, one day is as a thousand years and a thousand years as one day. The Psalmist put it this way: "For a thousand years in thy sight are but as yesterday when it is past, and as a watch in the night." Psalm 90:4.
It is important to observe that this statement is made by Peter in relation to the promises of God. He points out in verses 3 and 4 that some people scoff at the promise of the Lord's coming. Then in verses 8 and 9 he emphasises that even though a thousand years pass by, the Lord doesn't forget what He promised. It is like only a day to Him. In fact, in the next two verses Peter affirms: "The Lord is not slack concerning his promise, as some men count slackness ... But the day of the Lord will come." 2 Peter 3:9,10.