I don't agree with those who say that New Years Eve is just another day. It is not, it is an ending, the end of a solar cycle, another year has passed, and a new one is dawning. And it is a natural and good time for reflection.
God created the seasons, the days, the weeks months and years, for us to recognize their rhythms and differences.
Genesis tells us that each day is to have night and day. And each week seven days, six for work and one for rest. And God created the seasons as well, Genesis 8:22, "While the earth remains, seedtime and harvest, cold and heat, summer and winter, day and night, shall not cease.” The seasons are different, with different offerings. Winter gives us coolness and time for rest. Summer gives us heat and time for production. Spring brings the breaking of new life and the flourishing of beauty. Autumn warns us that the cold is on the way, and that we should prepare.
The seasons are all different and built into this world, they are not man-made ideas. They were created by God for humanity to observe and identify and understand their timings and differences, "It is the glory of God to conceal things, but the glory of kings is to search things out" (Prov. 25:2). God intended for mankind to study the different rhythms and times and structure our lives according to their different offerings.
The Bible itself reflects on the beauty of the differences of the days and what each new day brings us,
"22 The steadfast love of the Lord never ceases;
his mercies never come to an end;
23 they are new every morning;
great is your faithfulness.
24 “The Lord is my portion,” says my soul,
“therefore I will hope in him.” (Lam. 3:22-24).
Each new day brings new mercies, new grace and new beginnings. It is not just another day, it is a new opportunity to receive mercy and good things from the Lord, to face new challenges, to start again, and afresh.
Jesus himself reflects on this same idea, “Therefore do not be anxious about tomorrow, for tomorrow will be anxious for itself. Sufficient for the day is its own trouble" (Matt. 6:34). New days give us an opportunity for new beginnings, and as each new day will have its own problems, don't view them as just a continuation of progressing time, but as new and individual gifts from God. The end of night is a closing, the waking up in the morning is a new beginning. We are supposed to reflect on this.
Some Puritan might jump in here and say, but we aren't supposed to observe days.
"16 Therefore let no one pass judgment on you in questions of food and drink, or with regard to a festival or a new moon or a Sabbath. 17 These are a shadow of the things to come, but the substance belongs to Christ. 18 Let no one disqualify you, insisting on asceticism and worship of angels, going on in detail about visions, puffed up without reason by his sensuous mind, 19 and not holding fast to the Head, from whom the whole body, nourished and knit together through its joints and ligaments, grows with a growth that is from God" (Col. 2:16-19).
Paul is simply observing here that observing special days does not make you holier before God. But I am not arguing that they do. I am observing that each new beginning, each new day, week, month, or year, is a new offering from God, a new gift from the Lord above, to help you to contemplate, reflect and ultimately repent from what you have done wrong and look forward to a new day and a new beginning. Why do you think the Bible says not to let the sun go down on your anger? It is because God wants you to start afresh on that new day.
So, this New Years take the time to reflect and contemplate on your successes and failures in the past year. Reflect on the goals you have achieved and the ones you have not, and on the ways you have not maintained your faithfulness, and rejoice in the fact that the Lord gives you another year, a new start to work on these things again. Rejoice in the Lord who gives us these winding down of old days and these ramping up of new days. He is good to us.