Learn English – Get to doing something

I think the arguments on that site are pretty weak.

For one, the argument that "If you can't think of an example, there mustn't be one" is very poor. A lack of imagination does not constitute a robust argument.

In addition, the writer suggests replacing the pluralising 's' with a 'z', to get over the problem of singular and plural possessives. So, he's asking us to ditch the apostrophe and change pluralisation.

On top of that, the rationale for removing them are spurious at best:

1. Redundant: Hardly makes the case for this, as noted above
2. Costly: The idea that apostrophes makes up a considerable amount of a proof-reader's effort is bogus.
3. Snobbery: Removing the apostrophe will hardly bring about a revolution in attitudes. Snobs don't need tools to be snobs.
4. Text messaging: Citing the mores of txtspk as justification for eradicating a punctuation mark? Let's lose those pesky vowels, too, eh? Hell, Hawaii makes do with just 13 letters (if you include the 'okina (hello apostrophe!))
5. Impeding communication: I can't speak generally to this, but I've never come across a situation where the presence of an apostrophe has made it difficult to understand something. Nor have I struggled to express myself when faced with a potential apostrophe hole
6. Distraction: If the presence of misplaced apostrophes drives you to distraction, you probably have bigger issues to deal with than misplaced apostrophes.

Sure, sure, this is all pretty subjective. However, the very argument for removing apostrophes given on that site is riddled with straw men and subjective viewpoints.

In the absence of compelling reasons to remove the apostrophe, "legacy" becomes a very compelling reason to keep them.

Real reason

could work here.

The Oxford definition of real, in sense 2.1, is true or actual, and includes examples "his real name is James" and "my real reason for coming". It is contrasting the real (hidden or ulterior) reason with the apparent or obvious reason.

The 14-year old asked if he could help his mum wash the dishes, but his real reason was so that he'd be busy when his dad wanted help washing the car. This meant his brother would have to do it.

Here the boy is at least a little devious, but it can apply in a more neutral situation, where "ulterior motive" or "hidden purpose" would be less suitable.

Mrs Smith helps clean the church on Saturdays. She says it's to serve the community, but the real reason is she just likes a chat with the other ladies.

Here there is nothing devious. In fact, both reasons are probably true.

He told his wife he would be late home because he was extra busy at work, but his real reason was that he was arranging a surprise for her birthday.

This is probably used in a positive sense, although that depends on the surprise.