This situation has its roots in a little clause in the Treaty of Lisbon:
Taking into account the elections to the European Parliament and after having held the appropriate consultations, the European Council, acting by a qualified majority, shall propose to the European Parliament a candidate for President of the Commission. This candidate shall be elected by the European Parliament by a majority of its component members. If he does not obtain the required majority, the European Council, acting by a qualified majority, shall within one month propose a new candidate who shall be elected by the European Parliament following the same procedure.
Right back from its roots as the Parliamentary Assembly of the European Coal & Steel Community over six decades ago the European Parliament has been imaginative in how it exercises its powers. Back then, instead of sitting as national delegations, the Assembly members decided to sit as cross-national groups - the Socialists, Christian Democrats and Liberals. While I'm sure some would see this as reshuffling the deckchairs on the Titanic, this sent out a message that the Assembly members saw themselves as part of political groups first and foremost.
The Treaty is clear - the European Council proposes a Commission President, and the Parliament approves or rejects. So far, so familiar. There is nothing novel in this. What is novel is "Taking into account the elections to the European Parliament..." The main Europarties interpret this as them selecting candidates for the Council to decide on, taking into account who "won" the election.
In some ways, the structures of the European Union draw on the German ones. The European Council and the Council of Ministers are obviously based on the Bundesrat. And one feature of the German system is that in the run-up to federal elections, the two main parties announce their candidates for Chancellor.
In Germany, technically, the President proposes a Chancellor to the Bundestag, taking into account the election result (after all, it has to be someone who can form a Government), who can only take office after being elected by an absolute majority (in other words, "a majority of its component members").
Replace "President" with "European Council", "Chancellor" with "President of the European Commission" and "Bundestag" with "European Parliament" and see what you get.
The leading German parties are under no obligation to announce - or even select - candidates for Chancellor, but it just becomes part of the tradition.
There is one objection to Juncker you will hear - that his party, the European People's Party, didn't win the elections. True, and not true. In the United Kingdom we have become used to one party winning over half the seats in the House of Commons and forming a Government on its own. May 2010 was different - no party "won" the election and we were left with a House of Commons where the only realistic majority grouping was one comprised of the Conservatives and Liberal Democrats.
Across most of the rest of the EU, they are used to hung Parliaments and coalitions. Winning involves being able to form a majority with the support of smaller parties.
A second objection is that across Europe, people voted for anti-establishment parties. Well, yes, up to a point. If you take the two anti-establishment groupings, the European United Left-Nordic Green Left (which includes Sinn Féin) and the Europe of Freedom & Democracy (which includes the UK Independence Party), along with the group that Marine le Pen of France's National Front and Geert Wilders of the Netherlands' Freedom Party are trying to make, you still only have around one-fifth of the total membership of the European Union. We are looking at around two-thirds of Members of the European Parliament belonging to "federalist" groups.
One question you hear sometimes is "How do you vote out the European Commission?" There we have it - an Executive that we, the people, cannot remove. Proof that this is not democracy in action.
To which I can respond - "How do you vote out the Northern Ireland Executive?" Elections to the Northern Ireland Assembly can simply change the composition. There are rules on how the First Minister, Deputy First Minister and other members of the Executive are chosen in the Northern Ireland (St Andrews Agreement) Act 2006. The only anti-establishment party to gain representation is Traditional Unionist Voice, with just a single member of the Northern Ireland Assembly, namely their leader, Jim Allister, in Antrim North.
Of course, in the Assembly's inaugural election of June 1998, the Democratic Unionist Party were the anti-establishment party, the only main party opposed to the Good Friday Agreement, and while they took the two ministerial posts (Social Development and Regional Development) they were entitled to, they chose not to attend Executive meetings in protest at Sinn Féin being there. Less than a decade later, Northern Ireland had a DUP First Minister with a Sinn Féin Deputy First Minister - just goes to prove that when it comes to Northern Irish politics, never say "never, never, never".
Like the Northern Ireland Executive, the European Commission is an Executive which has changes in membership, but the basic structure - dominated by the European People's Party, the Party of European Socialists and the Alliance of Liberals & Democrats for Europe - remains the same. If you look at the Northern Ireland Executive, the reason for it being the way it is boils down to the sectarian divide, with it being important to ensure that Unionists and Nationalists/Republicans are represented.
And when it comes to the European Commission, it is the way it is so it ensures every EU nation is represented. This is not building a nation called Europe. If it were, then it would be an Executive formed the way it is across single-nation democracies. Juncker would be looking to form a centre-right coalition and hence be looking for support from the Alliance of Liberals & Democrats for Europe and the Alliance of European Conservatives & Reformists for a parliamentary majority. He would be unveiling an EPP/ALDE/AECR Commission (or maybe just an EPP/ALDE one with a confidence-and-supply deal with European Conservative & Reformist MEPs). The Progressive Alliance of Socialists & Democrats would be forming the Official Opposition. No doubt, for some more enthusiastic federalists, such a "normal" democratic structure would be welcome, but I prefer the way it is. The way the President of the Commission is nominated by the European Council and the fact that Commissioners are chosen by their national governments emphasises that the EU is ultimately a union of nations.
So, does Juncker have a mandate? Yes - and no. The Council is under no obligation to nominate him, but it is likely that any other candidate would be rejected by the Parliament. The Parliament has effectively bounced the Council into choosing him.