The brief version is that they believe that Raqqa should be used for their own forces in the U.S-led coalition and seriously object to any U.S. support to arm Syrian Kurdish Fighters, in which they want to push YPG gains and separate two of the Kurdish-dominated cantons.
A longer version as written in Syrian Kurds welcome U.S. arms, Turkey objects:
But Turkish Foreign Minister Mevlut Cavusoglu slammed the move, saying
"every weapon that reaches their hands is a threat toward Turkey," and
that Turkey's president would raise the issue during a visit to
Washington planned for next week.
[ ... ]
One plan Ankara has presented to Washington would have a Turkish-led
FSA force of around 10,000 push south to Raqqa from the YPG-held
border town of Tal Abyad. That would roll back YPG gains and separate
two of the Kurdish-dominated cantons.
Washington has so far been non-committal.
"We told them there are many alternatives for Raqqa and they didn't
disagree," said one Turkish official familiar with the talks. "They
said 'we understand your sensitivities, we don’t recognize their (YPG)
Turkey and its Syrian rebel force was "ready at any time to do Raqqa, after clearing al-Bab," the official said.
From the widely reported McCatchy report which has been cited when reporting about the Michael Flynn investigation. They provide a view from Ankara:
The view from Ankara
Turkey has angrily objected to U.S. support of Syrian Kurdish
fighters, arguing that to arm the YPG is to help a group that is
carrying out attacks on a key ally and fellow NATO member. The YPG has
ties to the Kurdistan Workers’ Party, or PKK, considered a terrorist
group by Turkey as well as the U.S. and the European Union. However,
the U.S.-led coalition considers the YPG the most effective military
partner against ISIS in Syria.
Turkey has insisted that the only feasible option to retake the
terrorist group’s capital of Raqqa is for its own forces to
participate in the U.S.-led coalition. The promise has been viewed
skeptically by the Pentagon, where it’s been dismissed as “Erdogan’s