In this article by RK-TECH they use the term "Synthetic" I don't know if they are talking about Groups 3,4 and 5 or just Groups 4 & 5. I believe it to be groups 4 & 5.
SUMMARY:
Synthetic Oils are engineered to withstand high heat without chemically breaking-down like their petroleum based counter-parts.
2 Stroke Oils are NOT subjected to the same level of heat of that of a 4 stroke oil.
Fuel, not oil, is the main cooling agent in a 2 stroke engine.
Oil, not fuel, is the main cooling agent of a 4 stroke engine.
Due to the method in which the oil is introduced, and the fact that it is not re-circulated, a synthetic based oil is not required to avoid oil break-down. The elements that mandate a non petroleum based oil are simply not present in a 2 stroke engine.
Synthetic oils are much harder to "burn" Usually, they do not burn. This is a problem is a 2 stroke engine.
Some Synthetic oil molecules CAN BE larger is size and can NOT penetrate (get into) the tiny areas that require lubrication (like lower rod bearings etc.)
Oil penetration is a necessity for bearing to survive under extreme load/heat.
There is one argument that many use. It is something like this: "Well, my exhaust valves stay much cleaner when using synthetic oil". Interesting... Ask yourself, What does clean exhaust valves have to do with bearing and cylinder lubrication?? Answer: NOTHING!
Please do not confuse clean exhaust valves with better lubrication. They are NOT related. In fact, the fact that the valves are clean lends credibility to the fact that the synthetic oil is NOT burning/combusting or penetrating small areas but rather just "gliding" over parts without impregnating in the parts (needed).
Oil must attach itself and penetrate into the "voids" of your engine. The smaller the oil molecule, the easier it is for this to happen...too large of molecule (synthetic) and it can not enter the needed/required areas. OIL is your engine's life blood!!
SIDE NOTES:
1) BRP/ Ski Doo quit recommending synthetic oil to be used in their snowmobile engines in 2006.
2) Synthetic Oil can NOT be used to properly seat piston rings. This is a KNOWN fact to the manufacturers of synthetic oil. MOST have a non-synthetic "Break-In" oil that is used to properly break-in a new engine.
3) AND the #1 reason why a synthetic oil is not as good in a 2 stroke engine--> IT DOES NOT FULLY COMBUST!
Your engine takes the energy from the combustion process to perform work on the crank train. This energy conversion is "fueled" from the Fuel/Air/Oil Mixture that it has available during the combustion process.
The Fuel and the Air will combust and be converted to energy.
The oil (if Synthetic) will not be converted to energy because it will usually not combust. So, this "oil" is taking up "space" in the head that will not aid with any energy transfer. Basically, DEAD WEIGHT!
Mineral oil WILL combust and aid in this conversion of energy! So, its energy is utilized!