A very valid argument. Sentiment runs very high in many parts of Orthdoxy to leave both institutions. The churches of Serbia, Georgia, Jerusalem, and Bulgaria have all passed resolutions or issued statements that to some extent reduce or eliminate involvement in the WCC. The monasteries on Mt. Athos have issued very strong statements in this regard.
The ROCOR has always held strongly that we should be involved in neither organization, and frankly this is the major sticking point in the efforts to restore communion between the ROCOR and the Moscow Patriarchate, now that communism has fallen. It wouldn't surprise me if the MP uses this restoration of communion as an excuse to pull out of the WCC, since the Russian hierarchy and laity seem not at all to be fond of ecumenism as it has been done in the past.
When the WCC began, leading Orthodox hierarchs and figures felt that it was the duty of the Orthodox to participate in order to give witness to the Orthodox faith. In retrospect, this was very faulty reasoning, but it is hard to put oneself back to that time today and predict what would happen. Consistently, the Orthodox have produced their own "dissenting views," to counterbalance the official declarations. At first, these where duly published, but with time the liberal cabal has more and more sidelined the Orthodox voice.
At the time that this happened, there was sentiment to withdraw, but there were many who felt that the WCC meetings were the few opportunities that Orthodox churches in the free world had to communicate with those Churches locked down under communism. Again, with hindsight, probably not good reasoning, since what often happened was the Soviet Union manipulating the Soviet bloc Orthodox churches into helping it pursue its political ends via the WCC.
At this time, there is no good reason to belong to either organization. It is clear that there is nobody in the WCC listening to what the Orthodox have to say, it is clear that there is no "iron curtain" preventing free communication with those churches in the former Soviet bloc, and it is clear that there are those, like you, who believe that our involvement in the organization implies that we agree with it theologically and politically. We do not, but it is not reasonable to expect people to come to another conclusion than that, and thus I and many, many others believe that we need to get out, and the sooner the better.
At this point, to be honest, most of what keeps us in is probably the combination of the Orthodox tendency to inertia and passive resistance rather than open conflict and high-profile sudden moves or statements. That and the fact that, as with any other church, there are people who have built their entire careers around ecumenism -- and those sorts of folks tend to have a bureaucratic mindset that allows them to effectively pursue infighting in attempts to protect their turf.
The Church in Georgia is completely out of the WCC, btw. Almost ten years ago, many clergy and monastics had a sort of uprising about it and Patriarch Ilia conceded membership.
The Georgian Church is very conservative and has an extremely strong monastic community. I say this from recent firsthand experience and discussion with several clergy and one Abbess, all of whom speak English.