If you could do anything then you could be perfect and a lot of people would be if it were true that they could do anything through god that strengthens them. Our moralities are imperfect also and most people do horrible things thinking they are in the right. If you could truly do anything through god who strengthens you the first thing you would do is acquire a perfect morality and teach it to the world. Being that nobody has displayed anything even close to the power of an all powerful god the statement is clearly false.
It's pretty basic logic- if you can do anything, you can't also be inherently flawed. Of course, these are the people who believe that an all powerful, all benevolent deity stated that all humans inherently deserve eternal punishment because their alleged ancestors disobeyed him in a manufactured scenario to which he already knew the outcome- a disobedience that their ignorance of good and evil as outlined in the story would make them unable to comprehend was "bad". Furthermore, that said "loving" deity is unable to forgive humans for the terrible crime of being exactly how he made them without a blood sacrifice- of himself to himself- and that this forgiveness is further contingent not on being a moral person but by believing the "right" thing. A belief that is determined almost entirely by where you are born. They then believe such a deity is just, righteous, loving, and deserving of blind worship and obedience.
So it's not like I expect logic out of such a belief system.
When the Bible states that..."I can do all things through Christ who strengthens me..", it is meant to mean that you can do anything that is logically possible.
In the same way, Since God is all-poweful, God cannot create a rock so powerful that he can't create. If God could create a rock more powerful than himself, that would go against his nature. In fact, God cannot even do everything. He can't lie. And he can't deny himself.
People should investigate the scriptures before coming to a quick conclusion. I can honestly say there is no contradiction in the Bible.
Hope what I wrote helped.
First, with all due respect, when you reference Philippians 4:13, you should include the whole context, and not just the specific phrase. Second, you are trying to juxtapose two completely unrelated concepts as a contradiction. They are totally separate concepts, and I firmly disagree with your interpretation. I would highly encourage you to read more into the book of Philippians.
The way I interpret Philippians 4:13 is that Christ gives those who believe in him and who ask for strength, the strength to ENDURE whatever hardship they may be facing. Just because you survive, endure, or are able to live with something doesn't make you perfect. Does surviving cancer make someone perfect?