The PRD says:
"At each new magus level, he gains two new magus spells of any spell level or levels that he can cast (based on his new magus level) for his spellbook."
But one my teammate is telling me that I can only choose spells that I am able to cast. It seems to me that the "spells of any spell level or..." means I can choose.
Any thoughts?
You get two spells. They do not need to be of the same level, hence "level or levels."
But you need to be able to cast both spells you select.
E.g. if you're a 10th level magus, you could could select two fourth level spells upon achieving 11th level, or you could pick a 4th and a 3rd. But not a 5th or higher.
In direct answer to your question, you can learn a 3rd level spell when you advance to 7th level.
You can't just select one small part of a sentence and ignore the rest of it. That sentence (as are pretty much all sentences) is to be read in its entirety, specifically the bit that goes "...that he can cast..."
So you'd need to be a 7th level magus to select a 3rd level spell. What it does mean though is that at 7th level you don't have to choose two 3rd level spells, you can choose 1 3rd level and 1 2nd level for instance.
The PRD says:
"At each new magus level, he gains two new magus spells of any spell level or levels for his spellbook."
But one my teammate is telling me that I can only choose spells that I am able to cast. It seems to me that the "spells of any spell level or..." means I can choose.
Any thoughts?
You posted the answer to your own question.
Here is the whole sentence...
"At each new magus level, he gains two new magus spells of any spell level or levels that he can cast (based on his new magus level) for his spellbook."
This sounds to me like I have a choice. I can choose spells of any level or spells that I can cast.
You're misreading the sentence. The magus "gains two new spells of any spell level or levels that he can cast...".
"Level or levels" isn't indicating you have a choice of spells of any level. It indicates that the spells you choose can be of the same level or different levels (a 1st and a 3rd, for instance,) so long as they are spells the magus can cast, meaning of the appropriate level.
At each new magus level, he gains two new magus spells of any spell (level or levels) that he can cast (based on his new magus level) for his spellbook.
The spell must be one the magus can cast. The OR is allowing you to choose 2 new spells that are not the same level. For example, a 1st and a 2nd instead of 2 2nd level spells.
You can choose spells that you can currently cast based on your magus level. If the spell is too high of a level to be cast then you can't choose it.
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You, 100%, cannot ever learn any spell for your spell list (divine or arcane) before you are capable of casting that spell. Full stop.
That's not entirely true. If you find a wizard's spellbook and decide to copy spells from it, even though some of them might be too high level for you to cast you can still copy them into your book (so they're there when you CAN cast them). I agree 100% that the OP is misreading the sentence in question. The free spells you write in your spellbook when you level up must be of a level you can cast (presumably because higher level spells are too complex for you to think of on your own until you get more experience), but as far as I can tell you can copy spells from other sources with no issue.
Here is the whole sentence...
"At each new magus level, he gains two new magus spells of any spell level or levels that he can cast (based on his new magus level) for his spellbook."
This sounds to me like I have a choice. I can choose spells of any level or spells that I can cast.
If it was meant to be read as you are interpreting it, the bit about "levels he can cast" would be entirely extraneous.
By definition, magus spells that he can cast are magus spells of some level or another (referred to in the text as "any level"). You could save word count by removing everything from "or" onwards and not lose any meaning. We can therefore reasonably infer that the inclusion of that clause adds meaning to the sentence. And the only reasonable meaning becomes "add magus spells of any level(s) he can cast".