The society will quickly change. The education system would be severely abreviated and simplified. Otherwise, it would be too spoilery if people can only get a university degree when they hit 23 years old or so. Further, there would be no teachers in the university alive for a time long enough for that.
The basic education would probably end when people reach their 10 or 12 years old of age. People would likely try some speciliaty/university courses that should be completed quickly, when people have no more than 20. Teachers should teach until they die. People should work until they die. There is no such thing as retirement.
Teens should engage in sex and have children as soon as possible, if possible when they are between 12 to 15 years old. The reason is that people who have kids in their twenties will have no time to educate their children and see they grow up. Also, each couple should be able to raise several kids and be able to at least start the education of the youngest one, so the first baby should come very early. Kids should start dating when they are still in their infancy, possibly when aged between 7 to 10 and should avoid breaking up or divorcing at all costs. If some couple breaks up or divorce, they should be incentived to get new partners as soon as possible if they still didn't reach their twenties. Since people would and should engage sex in their teen years and the life is too short to suffer major consequences from that, open/poly relationships and sex parties will be much more common.
People would start taking serious jobs still in their infancy. Six or seven year old kids should get the simplest jobs that don't need brute force or complex thinking. Most people start in their life jobs when they are 14 or 15. Bosses, CEOs and people involved in strategic jobs should be able to reach their positions when they are between 17 to 20 and eagerly teach as much as possible to their children/successors that will take their positions when they die by turning 25.
The society and everyday life would be severely damaged and will recede significantly since people are much less able to accumulate sophisticated knowledge and there are much less reasons to do so. Knowledge will also be much more scattered and more people would be needed to do a single job that in our elderly society someone in their forties could do lonely with enough experience. This also mean that people should be much more team workers - Many teams of trainees and juniors.
Also, the life is short, so people would likely try to live it the best possible. People would really hate time-consuming things. Carpe diem! Since dangerous behaviours that could make you get problems in the future are much less a concern, teens would likely drink alchool, use drugs, smoke, engage in (possibly unsafe) sex, engage in violent behavior and enjoy parties much more than in our common eldery society.
Most of the top government positions would be filled by people which starts when they are somewhere between 15 to 18 years old. Those people received special education for their jobs, likely being tought directly by their predecessors with the explicit purpose of replacing them someday. This would likely create an aristocratic society - only people who received special education for being able to fill government positions are eligible to fill these positions. Further, people who are deemed incompetent, unfit, untrustful or too old by the rulers are excluded from the possibility of succeeding them. However, the population would still be likely to be able to vote in the people who were not excluded from the sucession line. Further, since there are no people with much experience or with enough time to create a power network, it is likely that the population would be able to vote for many important things. Also, it is likely that people will be able to vote when they turn 10 or 11.
Also, if people knows exactly the day that they will die, people who are near enough (i.e. 23 and 24 years old people) would likely go crazy. Many 24's will likely engage in criminal activity, risk their lifes doing irresponsibly dangerous activities, do crazy things or simply going nuts. Many of those people would go nuts trying to do as many things as possible in the least time as possible when they still are living. Many people in their twenties would likely get severe obsessive-compulsive psychological disorders that only get worser and worser everyday.