You're free to have your preferences, of course, but synthetics, per se, are not the problem. Solo-WR400 has it half right, those troubles come from using the wrong oil, but "car" oil isn't necessarily the problem either. Both statements are an over generalization.
Yea, i've heard of too many clutches that were "questionable" as far as overall condition, slipping after swapping to a full synthetic based lube. If you know you have a clutch in solid working condition, you most likely won't have any issues. It's just my preference.
The "bad" oils are ECII (API Energy Conserving Group II) oils. These oils contain friction reducers that may cause a wet clutch to slip or behave badly. It also happens that nearly all of them are synthetics and blended for cars, too, ergo, "synthetic car oil is bad for your clutch". Bad logic.
The best oils available for a YZF are nearly all synthetics or petro/synthetic blends. However, none of these are ECII, and most either comply with or are labeled as JASO MA. One of the elements of the MA standard is compatibilty with wet clutches through the establishment of a minimum friction coefficient. Such oils are, then, certified compatible with any wet clutch system in any motorcycle. Car oils not labeled ECII are probably fine in that regard, synthetic or not.
Car, and even truck oils, do have one weakness, however, and that is shear stability. Multigrade oils are thin oils with additives blended in to keep them from thinning with heat as much as they should, so your 10w-40 looks like a 10wt at 70 degrees, and like a 40 at 210. Transmissions physically tear these additives apart, and the oil can become a 10w-20 in an alarmingly short time. The best motorcycle oils, like Amsoil, Mobil 1 Racing 4T, Golden Spectro 4, and others use viscosity improvers made for gear lube. These cost more, but hold up far better, and are well worth the difference.