The Buddha said “Those who see the Dhamma see me!” and this saying brings, for me at least, certain contemplations, for instance how seeing one “thing” shows the full extent of another “thing,” but if we contemplate this when reflecting on the reason why the three events are celebrated together, we may see why those who see the Dhamma see the Buddha.
When reading the Sutta’s not all of them are deep philosophical treaties, or about a deep philosophical matter, quite a few are about how to live, or how to live, and how the Buddha lives, some even show the Buddha seemingly nasty, or telling people off, however, we need to remember or think why would the Buddha scold someone, or why would a parent tell their child off? The Buddha may have been and enlightened being, but he was faced with people who were training under his direction who were not enlightened, who had ego’s, & needed corrected at times, and different circumstances require a different methods for disciplining those at fault.
The Sutta’s don’t show a hot and cold person but a person who acted appropriately with the circumstances he was in, and this leads me to the start of the reflection, the Death, Birth, and Enlightenment celebration of Vesakha.
Why are the three events celebrated together? I believe the three events, are celebrated together as each event (Birth; Enlightenment; & Death) signify the same things, the inconsistency in life, the benefits of enlightenment, and the way to live & die. Each phase in Siddhattha Gotamas life demonstrate different ways to live, or different useful traits to employ and we can use these examples ourselves, sometimes we are the trainee, other times the expert; the teachings and example the Buddha gave as The Blessed Buddha are useful for many aspects of life, and his example of resoluteness, as an unenlightened bodhisatta, is useful for anyone learning a skill.