Initial contact: Klingon assaulted by humans.
Events that follow: Humans try to help Klingon.
End result: Ultimately, humans assist in providing Klingons with important information.
First Contact: Disastrous
The Andorian Incident:
Initial contact: Andorian assaulted by humans.
Events that follow: Humans try to overtake Andorian party.
End result: Ultimately, humans assist in providing Andorians with important information.
First Contact: Positive
HUH?
For the Klingons, having to be helped by another culture is an act of dishonor -- "Gee, those Klingons can't take care of themselves, so we'll give them a hand." BAD!
For the Andorians, the fact that another race -- in their mind, subjegated by the Vulcans -- not only is sympathetic to their "cause", but gives them the proof they need of Vulcan treachery, means that the humans are after the truth: not just staying on good terms with their "mentors"GOOD!
That's what I usually go with.
There's also the circumstances of the first contact that have to be taken into account. The Klingons were bordering on civil war thanks to the provokations of the Suliban. Aside from the leader of the High Council and maybe a couple of prominent councilors, everyone else seemed convinced that it was Klingon against Klingon. Suddenly, the humans help show them all that it is a less-advanced alien race that is causing the problems. How embarrassing for the Klingons to be shown this with the help of outsiders.
The Klingon first contact differs from the situation with the Andorians. There were two races pitted against each other: the Vulcans and the Andorians. Here, the Andorians knew that the Vulcans were up to something, but they could not prove it. It took the outsiders to the conflict (and allies of the Vulcans) to put the situation right by exposing the Vulcan deception. There's no embarrassment here on the Andorians' end of the deal because they were vindicated in their suspicions. The embarrassment is on the Vulcans' end since they were exposed as going against the Vulco-Andorian peace treaty.
Essentially, humanity's interaction with the Klingons was an internal affair of the empire. Outside help, to them, was not warranted and probably unwelcome. Humanity's involvement in the Andoro-Vulcan conflict was not an internal affair. While their help was not welcome, the Andorians appreciated the help from the humans. It didn't cause embarrassment to their culture as it did the Klingons.
Ah ...