Voddie also talked about some of the distorted teaching of this day and age, namely the "prosperity gospel" that distorts Christianity into health, wealth, and material things all as a sign of blessing, or more specifically, redefining our purpose as existing to acquire things (as told in books like "The Secret" and other works aimed at nominal Christians.) The false teaching here is that God is little more than a genie listening to us, granting us whatever we like. Our mainstream culture is anxious about getting "things", when Christ taught the exact opposite. And beyond just things, the thinking can also extend into marriage, that finding the perfect partner will be the satisfying end (until the point that the person says, "they don't satisfy me" [in an eternal sense, they never will]).
Verse 27 speaks about how anxiety is unproductive, and how, as an example, anxiety in a marriage relationship can be compounded, or unnecessarily multiplied (e.g. spouse is upset over something, husband isn't, wife expresses concern that husband "doesn't care", etc, etc..) This is a good point, and I think it really hit close to home for a lot of people (self included... :)
He also pointed out that anxiety is ultimately a symptom of faithless self-reliance. Verse 28 speaks about how God has given us life, and yet we still do not believe that God can meet our EVERY need, no matter how insignificant. The false distortion of this is that if you see God's kingdom that he'll give you treasure and riches. As Voddie pointed out, you don't do "A" to get "B". You do "A" and don't worry about "B". At a very basic level, this text is talking about God's provisions of clothing and food (the basics) and not gold, jewels, sports cars, mansions, etc. God will see to it that you have food and clothing. I'm reminded of another message on this text, too, that talks about the DAILY reliance that we should have on God for provisions of food and clothing. It's not something to pray about once, but rather daily, as the Lord's prayer states, "give us this day our daily bread", which implies a daily reliance of God to provide for us.
Statistics show that one-half to two-thirds of the world live on roughly $2 a day. In light of the "prosperity gospel" of seeking spirituality for wealth and treasure, are we to assume that those in this poor population are not "seeking the kingdom"? Of course not. Americans are incredibly blessed and wealthy people, and this wealth can also be an incredible burden (and ultimately, an interference between us and God.)
To me, so much of this text brings home to me the message in works such as "Imitation of Christ", that talk in great detail of our sanctification by avoiding the material of the world to grow closer to God. Things of the world tend to be a hindrance in our walk, and there is considerable blessing in simplicity.
The text of Matt. 6:25ff should not be abuse: this is not endorsing a "prosperity gospel" that we should seek to grow closer to God in order to gain material "blessings." Rather, this texts speaks of reliance on God to provide for our basic needs such as food and clothing, and gives instruction to avoid fruitless, godless anxiety, which is nothing more than faithless self-reliance. Trust in God and know that He will provide for your needs.