The German citizens do not vote for the Chancellor and President. They vote for the party that represents them in the government (German Bundestag) It’s the members of the Party that has the majority who does.
We don’t vote directly for President either... we vote for electors... but as a ‘short cut’ we talk about the people voting in the President. If German citizens were backing Merkel their party representative would be lager and supporting her. I use the same language when referring to other ‘consensus’ groups like the Brits and Israel etc.