The best way to whisk egg whites is with large continuous strokes and conviction in a clean copper bowl with a large whisk with very thin wires made of stainless steel.
We regularly whisk organic free-range egg whites without any problem, and bearing in mind that in culinary history all eggs could once have been so described, it seems unlikely the egg is the problem.
A good, stiff meringue froth demands a complex interconnection of suitably distorted protein molecules.
Anything that interferes with the interlinking of the molecules leaves the whites an unappetizing slush. Oil is the usual culprit. Use clean, dry utensils, free of detergent.
Before the whites have formed a stiff froth, the merest drop of cooking oil, cream, or oily yolk that gets into the whites can ruin the meringue.
The eggs from our pet chickens, while not certified organic, are as close as we can get, and make wonderful meringues.
The problem, we suspect, is freshness. Whites from eggs less than 5 or 6 days old will not whip up. Supermarket eggs can be up to 2 weeks old, but the organic ones were probably newly laid.
This raises the question of what changes eggs undergo as they age to allow them to make successful meringues.
Eggs that do not whisk well may be too young.
The protein molecules develop cross-linkages as the egg ages, enabling the albumen to contain the air bubbles when whipped.