Yuck. I am not big on Marx, but I think he gets a lot right in his Critique of the Gotha Programme. Social democracy is more right-wing than the liberalism it purports to replace. Its intention is to maintain capitalist norms by bribing the poor with their own labor-product and using the capitalist state as the mediator, rather than giving them control over the natural wealth they are due. 

It is not even all that clear that social democracy is stable. It seems especially sensitive to rapid demographic changes (aging population, too low immigration, too high immigration, etc.) 

Rather than put band-aids on the fundamental inequalities in society, we should focus on the root of these inequalities in the first place. The class monopolies that states produce through the granting of privilege via its monopoly on the legitimization of violence are where we should look first. Why exactly does the capitalist class have such disproportionate bargaining power which allows it to exploit the working classes? Because the state used violence to give it these monopolies on resources, intellectual property, the movement of labor, and social institutions relating to finance. What happens when the state no longer gives them these monopolies? What happens when the capitalists must join the workers because their position and privileges have been degraded? That's a more interesting question! 

In my opinion capitalism is in some way necessary because people don't want take risks if there is no reward. So if everyone would own everything society wouldn't progress because no one would pay more taxes than others because no one would start up new companies and earn more money. That's why social democratism is the best possible social system.

That doesn't seem to be the right way though. Oppressing companies too much will hurt the workers in the long term and that is not very social at all. It seems more like a misguided attempt at reactionary governing than actual socialist policy.

I know that capitalism is not about competition. Pure capitalism seeks to dominate everything. The competition and stability is made by the regulation of the state.

My employer does make a profit from me. For that I do get compensated in a fair enough way. You say it yourself, exploitation doesn't have to be evil and is done by good people, sometimes with the best intentions. So why are you talking about it as if it was evil? Maybe it's a necessary evil to keep things going?

I had a very similar discussion with a hardcore neoliberal who would love nothing more than pure capitalism in all sectors. The truth is, you cannot slap a perfect system onto inherently flawed individuals. It doesn't work and will become unstable very quickly. You will have to have compromises to appease the most amount of people in the most moderate way. I think Germany found a very stable compromise. A compromise not everyone will agree with, but a compromise that will keep things running with a maximum amount of stability.

Changing sociopolitical conditions are not an argument for anything. Every single social and economic system is vulnerable to changing situations. It's about to be as robust as possible. And neither full capitalism nor full socialism are as robust as the compromise we have here.

The demographic crisis is just starting. China and Europe are both going to be hit hard in the coming decades because of the replacement rates and aging populations. If anything, mass immigration might be Europe's only option. 

Completely eliminating privilege is not the same thing as everybody having the same thing. It's the same thing as everyone playing on a fair field where all costs and decisions are internalized by those who make them and not put onto others without their consent. Human nature is a spook, and doesn't actually exist. There is no universal "nature" which can be ascribed to the 7 billion persons on this planet. Each individual has different wants, interests, goals, abilities, and disabilities. When we speak of "human nature" we gloss over that. 

There is no leveled play field since people have different capabilities... and although everyone likes to paint human as the most evil creatures on the world, you won't find species that take good care of the elderly to the point human does, won't find the level of empathy for the disabled, etc.

Who mentioned that everybody would own everything under socialism? Socialism merely is the premise that the workers in associated labor should control the productive capital which they use to perform that labor. People could and would still take planned risks because there are still rewards achieved by reducing the costs of production. It just so happens that you can only profit under socialism by actually reducing costs rather than externalizing them on to others. 

There are also many ways people can be motivated to achieve something without financial profit. 

People might take some risks with existing companies under socialism but they wouldn't make new ones with no chance of reward from their huge risk. That's just human nature.

Why wouldn't people association and dissociate into new worker's cooperatives for a variety of reasons? Competition (and therefore innovation) will still exist under market socialism, it just happens that the rewards are distributed to more people, and therefore more people have stake in reducing costs. Hence you'll still have innovation with the aim to reduce costs of production. There will still be profits in the sense of gains in productivity and wealth over the inputs.