But that's exactly what Germans have been trying
Nobody in Germany in a leading position said this as justification as to why Germany did not close the borders in 2015. If anything this was said as to why Germany might be able to integrate the refugees into the work force - which as the link showed turned out to be true. Merkel always justified her decision as necessary for stabilizing Southern Europe and preserving freedom of movement and the EU.
doctors and engineers
Another quote never said by Merkel and others in the context that is often implied. It is a fact that most refugees, particulary from Syria, are above avarage qualified, with a particulary high amount of doctors among them (again relative to their country) but compared to European societies those are rather low. During the Covid crises, quite a few German hospitals were glad to have qualified people from Syria though.
ridiculous - considering the fact that most of the "refugees" were young men
Young men are refugees like any other people too, particulary in Civil Wars like Syria.
Sarrazin helped pointing out some of the problems with Germany's integration system, particulary the difficulties for refugees from non-European countries to integrate. It his partly thanks to him that many reforms had been made, including language courses from day one and less restrictions on finding work. By the 2nd book however he went off the deep end, and started spouting a lot of racist antisemitic stuff.
A right-wing conspiracy nut-job who used to be a reapected journalist, but who eventually only published in the German Kopp Verlag (the one for Hitler apologists and alien believers).
that you made a mistake
A mistake implies that there was a better option available. Merkel had to choose in 2015 between
A) Close the borders, disrupting trade and causing economic harm to Germany and risking the destabilization of Southern Europe and the Balkans, with the EU's future in question
or B) letting the refugees in, knowing that Germany was capable of dealing with the refugees (and as a Bonus, staying true to her Christian conscious as a parish daughter).
B was in every way the better option. Humanitarian issues aside, preserving the EU is Germany's vital interest.