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 [contradict] 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:
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 / all powerfulness" is a misrepresentation of Scripture's representation of "The Most High". This makes the question "leading, (legal definition)" and "invalid" in the same sense as a prosecutor trying to trick a defendant into confessing robbery by asking, "When you robbed that store, did you think stealing was wrong?"
The power to keep all promises, to forget sin, to forgive all debts, and even the power to be absent - is actually evidence that God is "The Most High, (Most Powerful)" and cannot be forced by some other authority into breaking a promise, or contradicting himself in some way.
Scripture states that God limited his own power, by "swearing by himself" - because there was no other way to constrain his own power. This actually indicates that God has no choice but to be faithful to his own word, and is therefore trustworthy.
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 when God restrains himself by his own word - he is no longer /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.”
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 to fail - even himself; 2.) Wise: That God is "for us", an advocate, determined, and desperate, to impart life - even when 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).
Note 1: If God is "True" then as "truth" God cannot contradict himself, any more than a logical syllogism/truth could contradict itself.