When asked about whether or not Quinn would be up for some training, Quinn didn't hesitate to say yes. The reason being he knew he needed to get stronger. Facing Edward opened up his eyes a little. There was more to getting stronger than just improving his stats. Even if he was faster, more powerful and had more stamina, these things couldn't replace skill.
On top of this, the higher his stats were currently getting, the less of an effect the increase was having when comparing them to the strongest of vampires. This was always going to be the case, but he didn't realise it would become apparent so soon.
For example, when Quinn first started, he had five strength, when he became a vampire his strength had increased to ten. His power had increased by double with only five points extra. However, if his strength was at fifty, and his points increased by five again, it didn't quite have the same effect. His strength would only marginally increase, and it didn't have the same effect.