Essentially, you’ve walked up the natural numbers in order and noted that you encounter more multiples of 2 than multiples of 3. But there’s no reason to privilege that particular way of encountering elements of the two sets.
For instance, instead of mapping multiples of 3 to a close multiple of 2, we could map each multiple of 3 to two-thirds of itself. Then every multiple of 2 is accounted for, and there are exactly as many multiples of 2 as of 3. Or we could map even multiples of 3 to one third their value, and then the the odd multiples of 3 are unaccounted for, and we have more multiples of 3 than of 2.
Essentially, you’ve walked up the natural numbers in order and noted that you encounter more multiples of 2 than multiples of 3. But there’s no reason to privilege that particular way of encountering elements of the two sets.
For instance, instead of mapping multiples of 3 to a close multiple of 2, we could map each multiple of 3 to two-thirds of itself. Then every multiple of 2 is accounted for, and there are exactly as many multiples of 2 as of 3. Or we could map even multiples of 3 to one third their value, and then the the odd multiples of 3 are unaccounted for, and we have more multiples of 3 than of 2.