Why two people born the same day are nothing alike
Same date, same Sun sign, and almost nothing else in common. The reason is structural.
The standard objection to astrology is that everyone born on a given day should be identical. It is a fair objection to sun-sign columns and a poor one against charts, and the difference is worth understanding.
What a shared birthday actually shares
The Sun's sign, and roughly the positions of the slower planets. That is genuinely a lot of shared material, and people born the same week often do share a certain flavour.
What it does not share
The ascendant, which changes sign every two hours, so two people born the same day at different times have completely different house structures. Every planet in a different department of life.
The Moon can also change sign within a day, since it moves twelve to fifteen degrees every twenty four hours.
The place matters too
Born the same minute in Mumbai and in London, you have the same planetary signs and a different ascendant entirely, because the horizon is somewhere else. The houses shift accordingly.
The honest version of the objection
The strong form of the objection, that identical charts should mean identical lives, is not answered by any of this and astrology should not pretend otherwise. What a chart claims to describe is disposition and timing, not outcome, and two people with near-identical charts can make very different use of the same material.