There are a few classes you can multiclass into to gain skills, such as Bard, Ranger or Rogue.

In addition to that, in the player's handbook there is a feat called "Skilled" which allows you to gain proficiency in any combination of 3 skills or tools.

In Xanathar's Guide to Everything, we have the Prodigy feat which gives a skill proficiency and a few other things, but can only be taken by a Human, Half-Orc, or Half-Elf.

In Tasha's Cauldron of Everything, the feat Skill Expert gives proficiency in a skill and a few other benefits, with no racial prerequisite.

There is also a bard ability in the college of lore that allows you to learn 3 more skills at level 3.

Currently, the downtime rules allow you to gain proficiency in tools but not skills.

In case it isn't clear, you don't have to pick skills from your class skill list when you gain new skills through the "Skilled" feat. You can pick any skill you want.

You choose it.

As you said yourself, the list that presents your options has more elements than the number they tell you to choose. Rogue has 11 options available and you choose 4 from it.

The only thing you can't choose are the skills from the background and some racial skill proficiencies - but you can make a custom background that fits what you want, and if you already have one of the skills that you would get from the background, you can choose another skill freely.

If a character would gain the same proficiency from two different sources, he or she can choose a different proficiency of the same kind (skill or tool) instead.¹

In a sense, your sister isn't completely wrong - the set of available skills (to get proficiency with) from rogue can't be changed. As your question mentions, those are:

Acrobatics, Athletics, Deception, Insight, Intimidation, Investigation, Perception, Performance, Persuasion, Sleight of Hand, and Stealth

What you can change, though, is the subset of skills that you will have proficiency with.

Additionally, some races give you a specific skill proficiency, for example, elves get

Keen Senses. You have proficiency in the Perception skill.

But that's how far the Elf race goes in defining what skills you are proficient with - other than that, it's up to your class and background. Note that other races, such as Variant Human, might give you a free skill choice too.

About the lore and predominances

As you said, more often than not, a Dex rogue will be taking Acrobatics over Athletics. That doesn't mean they can't take athletics. From a lore point of view, your DM (or your entire table) might want you to justify your choices in your background, and some are easier to justify than others, but that's nowhere needed or forced by the rules themselves.

As a note, 5e has greatly reduced this kind of restrictive interaction. What I mean is that you can choose to be an Evil Dwarf Wizard. It's common in older editions or other systems to have some kind of restrictions. For example, if you were playing Paladin you would have to be Lawful Good. Or, if you look into games like World of Warcraft, only specific races can be played as some classes. That's generally not true for 5e - you can mix any kind of alignment, class, race, etc. without losing anything, just getting some not optimal improvements. This means the bonus you get from being a Rogue don't change whether you are a High-elf, a human or an Orc - what changes is just the bonus you get from being a high-elf, a human or an orc.

¹ Per Crawford, this only applies to background skills that you get at 1st level.

The proficiency rule for backgrounds applies when you gain your background at 1st level. It has no relevance outside that context.