I here assume a perfect Democracy in which decisions are taken according to the majority will of the people. In Anarchy everyone chooses directly for him/herself. Now what happens based on how many people feel your way?
On simple topics (theft, murder) more than 99% of the population agree anyways. In Democracy acting in violation will be illegal. In Anarchy the people that disagree would have to live among themselves and are to few to build a working society. If they don't want to live isolated or end up in jail they have to accept the rules of the many. The result is almost identical.
On minority issues (about 90% -10%) democracies enforce the will of the majority on the minority. The minorities are subject to the goodwill of the majorities and since people are on average nice, strong discrimination on minority issues is rare in democracies. However we see a broad indirect discrimination agains minorities. Anarchy allows these minorities to govern themselves and removes the rule of the many over the few.
Finally on split topics (about 50-50) like guns, religion, ... democracies always force a compromise. Any party will make legislation that half of the population is unhappy about. Anarchy allows for different ideas to exist in parallel. Let religious people live by religious law as long as they do not try to enforce it on others! We do not need a compromise if we can have it all.
Finally, if you are a social democrat, do not fear anarchy. Opposed to all other world-views we are not trying to force anything on you. You can still organise with like-minded people and live by the same rules as now. Since most political opponents will leave you can probably even go much further. Just please leave us out of your system.
Interestingly, anarchy will now allow for a competition between systems. You should only fear anarchy if you think that your system will fail and can only be supported by forcing people to live their live as you have envisioned it for them. But if you believe it will fail, why advocate for it?
