On Friday, the free world’s two most important leaders met at the White House. Chancellor Angela Merkel of Germany needed reassurance. President Trump needed a public-relations win.

Neither got what they hoped for.

We’ll see what leaks emerge, and we’ll surely hear plenty of spin, but winter hung on at 1600 Pennsylvania Ave., with frosty body language and icy words.

That’s bad news. There are four leaders who really matter today, and two are our enemies, Vladimir Putin of Russia and China’s Xi Jinping. We in the West need solidarity between the other two, Angela Merkel, the de facto leader of Europe, and Donald Trump, on whom the weight of global leadership still sits uneasily.

Quarrel as we may over lesser issues, the United States and Europe need each other. We can’t go it alone, and neither can they.

Merkel came to Washington with three items on her agenda: to warn Trump against Putin (whom she’d pegged from the start); to convince the president that NATO is indispensable, and to defend German industry and trade. Putin wasn’t mentioned by name at the joint press conference, but the chancellor pointedly brought up the Ukraine crisis, laying down her marker.

She’s going home with all the worries she had when she arrived.

For his part, President Trump needed public positives after a bruising two weeks. He tried to portray Germany’s agreement to increase defense spending as a personal win, but Germany had embarked on that course long before Trump was a nominee.

Then, taking journalists’ questions, he clung to his claim that he’d been wiretapped by former President Barack Obama, stepping on potentially positive headlines.

As for NATO, political hogwash is being spewed in rivers. Yes, NATO states could do more, but comparing GDP percentages is misleading. While we spend about 3.6 percent of GDP on defense, we’re a superpower with interests all over the globe.

If you break out the proportion we have committed to NATO today, it’s 1 percent or less of GDP, lower than those “freeloading” Europeans.

NATO states don’t “owe vast sums.” The 2 percent of GDP target is voluntary, not a treaty commitment.

For her part, Merkel went out of her way to speak well of the United States and to express German gratitude.

She grew up in former East Germany and understands how monstrous Soviet tyranny really was. Merkel values freedom. Careful to keep her remarks non-controversial, she was nonetheless firm and principled. She badly wants this relationship to work.

But personalities, too, are strategic factors. When the president and the chancellor met, it was a trip to the dentist for both of them.

Merkel views Trump as a bull in a dangerous china shop, and Friday’s talks didn’t change that. She’s not used to Trump’s enthusiasms and flamboyant behavior, his rejection of convention or his bluntness.

For Trump, she’s something new, too. Merkel probably has the highest IQ of any major world leader, but she never flaunts it: The old German dictum, “Mehr sein als schein,” “be more than you let on,” defines her approach.

Trained as a physicist, she’s reserved, steady, analytical, detail-driven and sly. Frau Merkel is one tough Kuchen.

Americans see her through the lens of her immigration error, when she briefly opened Germany to refugees without limit. That did cost her some support, but she’s still on track for a fourth terms as chancellor.

Germans see her as trustworthy, reassuring. She’s stood up to Putin, saved the euro, held the European Union together and delivered a healthy economy. Her nickname among the electorate is Mutti, which translates as “Mommy.”

Other Europeans may not love her — they’ve felt her toughness — but they respect her.

With Britain stuck in the turmoil of Brexit and losing influence, Merkel is Europe’s leading political figure — and she’ll go the extra mile to work with Trump. But the president has to recognize her worth and make an effort.

The Friday meetings did not advance our relationship. On the contrary, the encounter portended food-fights on trade and more concerns about NATO.

Putin, who wasn’t there, was the only winner.

Ralph Peters is Fox News’ Strategic Analyst.