Warsaw's suggestion to donate it to Ukraine instead has left Berlin concerned about further NATO involvement in the war in eastern Europe, while domestic critics believe the move was a mistake.
An anti-missile system Germany offered to send to Poland should instead go to Ukraine, Warsaw said, raising concerns that such a move would signify an escalation of NATO involvement in the war in eastern Europe.
Others believe the Polish government's rebuff was a mistake.
Poland's surprising response to Berlin's offer was welcomed by Kyiv, desperate to protect its airspace as continued barrages of Russian missiles have knocked out power across the country.
But Germany's Defence Minister Christine Lambrecht stressed that the use of NATO defence systems outside its territory needs to be agreed upon by all member states.
"It is important to us that Poland can rely on allies to stand by each other, even in difficult times, and especially Poland in its exposed position," Lambrecht told reporters in Berlin.
"That's why we have offered to support air policing and Patriots, but these Patriots are part of an integrated air defence of NATO, that is, they are intended for NATO territory," the minister said.
"If they are used outside the NATO area, then it has to be agreed with NATO and with the allies beforehand."
In Poland, critics of the populist ruling party, PiS, accused it of sacrificing the country's security with a war next door in Ukraine for the sake of a domestic political struggle which exploits anti-German sentiment for short-term gain.
The Rzeczpospolita daily newspaper called the new proposal by Poland's leaders "shocking," arguing that it would require sending German soldiers operating the system to Ukraine.
"That, in turn, would involve NATO in a direct clash with Russia, something the alliance has been trying to avoid from the beginning," deputy editor Michal Szuldrzynski wrote.
"This proposal affects Poland's credibility and, worst of all, its security. The Germans get a clear signal that we do not want their help, so the defence potential of the Polish sky will be lower," according to Szuldrzynski.
"In the worst war in Europe since 1945, this is an unforgivable mistake."
Duda not asked to weigh in
An aide to Poland's President Andrzej Duda said the president had not been consulted on the decision. The president is the supreme commander of Poland's armed forces and has a say on matters of national security.
Duda believes that if the missiles are made available by Germany, regardless of where they are placed, they should, first of all, protect Poland's territory and the Poles, Duda's chief of staff Pawel Szrot said.
The PiS party, facing elections next fall with its popularity dented by 18% inflation, has been ratcheting up its anti-German messaging, long a staple of the party's campaign rhetoric.
Party leader Jaroslaw Kaczynski has also been trying to link his domestic opponents, particularly Donald Tusk -- a former EU leader -- to Germany, saying Sunday that if Tusk's party wins next year, Poland will find itself "under the German boot".
When Germany recently offered Warsaw Eurofighter planes and Patriot air defence missile batteries, Poland's Defence Minister Mariusz Blaszczak initially said it was an offer he would accept with "satisfaction".
The offer came after two men were killed when an apparently stray Ukrainian defence projectile fell in Poland near the border with Ukraine on 15 November.
But Poland's tune changed after Kaczynski gave an interview to the state news agency PAP on Wednesday, saying that the offer is "interesting," but that "it would be best for Poland's security if Germany handed the equipment to the Ukrainians."
Since then, both Blaszczak and PM Mateusz Morawiecki have repeated the position of Kaczynski, the country's most powerful leader.
Kaczynski 'has gone mad', opposition leader says
Tapping into anti-German feelings has long been a political strategy to win votes in Poland. Older Poles still carry the trauma of the atrocities inflicted on Poland by Germany during World War II.
With the election campaigning underway, Poland has been demanding €1.25 trillion in wartime reparations from Germany — a bill Berlin says it won't pay.
Kaczynski also blames Germany for supporting EU efforts to defend the rule of law in Poland and reverse changes to the judiciary by withholding funding.
Meanwhile, Russia's invasion of Ukraine has created new strains. Poland was long a critic of Germany's gas deals with Russia and has also been critical of Berlin's initial hesitancy to arm Ukraine.
In Poland, some critics pointed out that the government was not only refusing higher military protection but also turning its back on critical EU funding, billions of euros that have been held up by the government's refusal to follow EU guidelines on safeguarding the independence of judges.
Marcin Kierwinski of the opposition Civic Platform party said Kaczynski "has gone mad" for "rejecting" the Patriot missiles and EU funding "during war and crisis".
After Russia's full-scale invasion of Ukraine on 24 February, NATO beefed up its defences along its eastern flank, including Poland, while Warsaw has worked to strengthen the nation's own military with massive armament purchases.
NATO deployed US Patriot batteries to Poland and German Patriot batteries to Slovakia, as well as a French equivalent system to Romania.
NATO's policy is not to get directly involved in the war and to deploy the batteries only to protect member countries.