In the first part of v. 12, Paul was referring to his goals mentioned in Philippians 3:10. He had not reaching the point of completion yet. He was not perfect. I, personally, would consider him spiritually mature. Far more mature than I. So it is interesting that he is admitting he has not reached the quitting point yet. He was not done growing. One of the marks of spiritual maturity is realizing you still have much to learn and gain from Christ. You're not done yet. Paul was admitting to this truth..."I'm not done growing yet."
This says a lot to me. If Paul was not done growing yet, then I am far from being done. There is so much to learn and gain from knowing Christ. How many times have I read a single passage and God convicts or challenges me on way. Then later (weeks, months, years later)...I can read it again and there is a totally different conviction and challenge. There is so much to learn. Or in my preaching...I do not hesitate to preach a message or part of a message I've already preached in the past. Seems every time I preach it, something new is gained. There is a new conviction or new challenge. I approach it from a different perspective. Probably because I have spiritually grown since I last preached it. There is so much to learn and gain from knowing Jesus!
And then Paul states "but I press on". The word "press" in the original Greek is the word "dioko". It is translated in other passages in the N.T. as "to pursue" or "to run after". The idea here is that Paul does not take a "whatever" approach to spiritual growth. He "runs after" it. He pursues it. He pretty much states the same thing in 1 Corinthians 9:26-27 when he says, "I do not run like a man running aimlessly; I do not fight like a man beating the air. No, I beat my body and make it my slave so that after I have preached to others, I myself will not be disqualified for the prize." Paul was serious about spiritual growth and pursuing, "running after", Jesus. He was intent on keeping his eyes on Jesus the author and perfecter of his faith (Hebrews 12:2).
I want to be like Paul. I want to be serious about pursuing or "running after" Jesus. How? I think it gets back to the basics that apply not only to me, but to anyone who is serious about growing and deepening their faith. A consistent and regular intake of and obedience to Scripture. Prayer. Christian fellowship. Being on guard as to what goes in my eyes and ears (and thus my brain where my thoughts come from.) Corporate and private worship. Being on the front lines of evangelism. Tithing. To remove or limit any of these will result in spiritual deprivation, malnutrition, and eventually spiritual apathy.