Beitzah 3: Fruit and Eggs

[Edited to add: My apologies - I thought this posted hours ago, and was surprised to discover it pending still. -AG] What makes the egg that is laid on yom tov problematic? Well, perhaps it compares to other decrees - for example, to not pick fruit in violation of the prohibited labors on Shabbat/yom tov. But the cases are not entirely parallel to begin with - and the decree wasn't in place on both eggs and fruit equally. Maybe this issue is the liquid that seeps out from fruit... But how parallel is that seeping liquid from fruit really parallel to an egg? Or maybe there are other ways that the egg and fruit are similar. Also, the notion that the egg is off-limits because it counts as preparation - which might well then be a Torah-prohibition, for which even a doubt or question is treated with care and stringency. As compared to rabbinic prohibitions, which would be treated with greater leniency. That leads to a case for consideration of a chicken that isn't laid on the holiday, but that it might have come from a trayfa - a non-kosher bird. [What's What: safek d'Orayta le-chumrah, safek d'Rabbanan le-kulah, cases with a lack of clarity]