#1. Question Restatement:

If God really is "All Powerful", then why can't he deny himself? Or, is 2 Timothy 2:13 actually saying that God "will/would not" deny himself - even though he can?

ESV, 2 Timothy 2:13 - if we are faithless, he remains faithful— for he cannot deny himself.

This question appears to be related to another based on Hebrews 6:18, (Interlinear), suggesting that God "chooses" not to lie, rather than is incapable of lying. That same analysis of the Greek is invalid - for the same reasons it is invalid in this context:

http://biblehub.com/interlinear/hebrews/6-18.htm

2. Greek Analysis:

2 Timothy 2:13, (Interlinear), does not carry any "subjunctive, (Wikipedia)" sense of "perhaps", "probably", or "may not" - or even some "personal intent".

The text uses the Greek word, "δύναται" which certainly conveys a sense of "ability", "capacity", "capability", "power" - not "will", or "authority".

The "Will" of God is not expressed as "δύναμαι":

NASB, 2 Timothy 1:1 - Paul, an apostle of Christ Jesus by the will of God | διὰ θελήματος Θεοῦ, according to the promise of life in Christ Jesus,

3. Explanation - God is not "All Powerful", but is constrained by his own promises:

God's "omnipotence" is a misrepresentation of Scripture - which makes this question "leading" and "invalid". This means that any analysis of a possible use of the "subjunctive mood" is irrelevant - because the basis for the very basis for the question is invalid.

Scripture states that - "God swore by himself" - to show that God had limited his own power, and that he didn't actually have the power to overrule or deny himself - so that his promises would be trustworthy and absolute.

It is a false equivocation to say that "being the Most Powerful" is the same as being "All Powerful": if the only thing in reality that could cause God's power to fail is himself, then it makes him the /most/ powerful - the "Most High" - but if God is restrained by his own word - he is not /all/ powerful.

NASB, Genesis 22:16 - and said, “By Myself I have sworn, declares the Lord, because you have done this thing and have not withheld your son, your only son,

NASB, Isaiah 45:23 - “I have sworn by Myself, The word has gone forth from My mouth in righteousness And will not turn back, That to Me every knee will bow, every tongue will swear allegiance.

NASB, Jeremiah 22:5 - But if you will not obey these words, I swear by Myself,” declares the Lord, “that this house will become a desolation.”’”

NASB, Jeremiah 49:13 - For I have sworn by Myself,” declares the Lord, “that Bozrah will become an object of horror, a reproach, a ruin and a curse; and all its cities will become perpetual ruins.”

4. A Leading Question, a Strawman Fallacy:

This question is "leading" in that it is "presupposing" the validity of an absurd misrepresentation of Judaism and Christianity.

There is an intentional misrepresentation that atheists make about "theism" in order to create a false conundrum, to have an easier argument to refute, but:

Scripture does not at all state that God is all powerful, all loving, and all knowing. Theists immediately recognize the claim as a misrepresentation of who God is - especially in view of so many references, for example:

NASB, Isaiah 43:25 - “I, even I, am the one who wipes out your transgressions for My own sake, And I will not remember your sins.

NASB, Hosea 4:6 - My people are destroyed for lack of knowledge. Because you have rejected knowledge, I also will reject you from being My priest. Since you have forgotten the law of your God, I also will forget your children.

Actually: Scripture emphatically restates, over and again, that God is 1.) Faithful: That God is true, "The Most High" ensuring that nothing can cause any of his promises fail - even himself; 2.) Wise: That God is an advocate determined, and desperate, to impart life - even then there is so much death. 3.) Just: That God judges people according to their own mercies - or else by their own condemnations;

To parents - it is immediately obvious what these three attributes entail: "love", (the faithful determination for life, and the desperation to advocate for pardon).

2 Timothy 2:11-13 is simply a restatement of those precepts:

NASB, 2 Timothy 2:11-13 - ["Wise"] 11 It is a trustworthy statement: For if we died with Him, we will also live with Him; ["Just"] 12 If we endure, we will also reign with Him; If we deny Him, He also will deny us; ["True"] 13 If we are faithless, He remains faithful, for He cannot deny Himself.

Qualification: Note, "if we died with Him" is an appeal to imitation of Christ, (Christianity) - which is: the unconditional advocacy for life and mercy - and the forfeiture of any "right" to condemn.