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A brief web search attributes the quote to Neils Bohr (the guy involved with the Bohr-Rutherford model of the atom). The source of the quote isn't terribly important, but it was an interesting tidbit if true.

The full quote from Neil allegedly is: "There are trivial truths and there are great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true."

Allegedly he has another quote related to this: "A great truth is a truth whose opposite is also a great truth."

Another version of the quote from Neil: "The opposite of a fact is falsehood, but the opposite of one profound truth may very well be another profound truth."

There seems to be either a case of broken telephone or that Neil shifted and toyed with his position over time. Supposing all of the quotes are actually his, and that OP's quote is also directly from Neil, it stands to reason that Neil was proposing that there was necessarily at least two "great" truths that stood in opposition to each other. We can test this hypothesis, but first we would need to know what the heck a "great truth" is.

I propose the easiest way to reconcile this is by interpretation "trivial truth" to be some kind of quantitative measurement that reflects reality. E.g. "this pencil uses 0.7mm graphite". While "great truth" is a qualitative assessment. E.g. "the cat is big" is true, but so is the opposite "the cat is small". It depends on a frame of reference.

The proposal is a best guess. Maybe Neil explained what he meant at one point.

Is it though? How about some examples.

At face value I don't agree with the premise in the quote, but I enjoy this kind of conversation starter. Highly encourage posting more things like this.