I don't know if this is a constructive question per the site's definition. It is right on the line between being a "Pastoral Advice" question and something that can be answered doctrinally, but since it can be answered partly based on Scripture (and partly based on subjective reasons) and the fact that these principles are generally applicable and agreed upon my Christians of all walks, I'll give it a shot.
The most probable reason is also the most subjective: Because we are appreciative and thankful for specific things.
Addressing your request that is simple enough for a child to understand, the above is probably simple enough for a child under the age of five or so. The rest is probably too much for that age, but may be OK for kids that are older. It helps if they know the verses, and the rest explains things in more human terms, using the verses as a framework.
It's the same reason my kids thank me when I surprise them with a trip to the park to play, or a trip to the ice cream shop. It's why I thank my wife when she cleans up a mess the kids made so I don't have to or vice-versa. Because we understand the value of little things, and because we love each other and want each other to know we are appreciated. If we love God, we'll do the same. It's just a natural extension of love and a thankful spirit.
As far as reasons that can be backed up Scripturally: (These Scriptures lay out principles that tie in to the ideas in the more subjective section that follows them.)
1 Thessalonians 5:18 (King James Bible (Cambridge Ed.))
In every thing give thanks: for this is the will of God in Christ Jesus
James 1:17 (King James Version)
Every good gift and every perfect gift is from above, and cometh down
from the Father of lights, with whom is no variableness, neither
shadow of turning.
The meat of your question seems to be in this area: If we believe in free will, how can we think that God gave us each individual specific thing, so I'll address that here.
Note that the belief in free will does not nullify the preceding Scripture. The belief in free will is one of the foundational beliefs in my perspective, but I still believe all good things come from God.
To those of us that believe that sin and suffering are a result of man's free will, it doesn't nullify the fact that in order for something "bad" to happen, God has to allow it to happen. There's a difference between allowing something to happen and causing something to happen. In His sovereignty, He is certainly capable of intervening to stop a situation, or to manipulate the situation to alter our decisions.
We don't deny His sovereignty. Free will isn't incompatible with the Sovereignty of God from an Armenian perspective.
With this, we also accept that the good things come because He has allowed it, or that He has caused circumstances to be such that that the good things have come from Him.
Getting back to more general reasons we give thanks for every little thing, now that the above portion has been addressed...
1 Thessalonians 5:17 King James Bible (Cambridge Ed.)
Pray without ceasing.
The last one may not be obvious to everyone as far as why it's relevant here, but one of the easiest ways to pray throughout the day is to simply get in the habit of praying a quick prayer of thanks for the little things, like the ones you're asking about. Getting back to the subjective (but remaining in the realm of common sense that most people would agree with)... This is a wonderful way to keep God in your thoughts, to keep your relationship strong.
It also helps us to cultivate that thankful, loving, and kind spirity that we Christians should have.
More subjective - applied psychology or common sense, take your pick
As a side note, keeping God in our hearts and being thankful is a great way to help us to resist temptation to sin. If we are constantly thinking of how great God is, and keeping an inventory of the good things He has done for us (great and small), when temptation arises, we should be thinking "If God has done all this for me, how can I possibly want to do this and make Him angry.
This is what we should feel for our employers if we think of stealing from them, or what our kids should think of us before they do something that will make us ashamed of them. It's simply not wanting to hurt/shame/dishonor someone you love.
Saying constant prayers of thanks helps us to remember that He does do those things for us. And the more we love and appreciate Him, the less we should want to hurt Him, dishonor Him, or know that He is ashamed of us.
Finally, we shouldn't be just thankful for the "good" things in our lives. We should be thankful for everything, even those things that we don't think are good right now.
*Romans 8:28 (KJV) King James Bible (Cambridge Ed.)*
And we know that all things work together for good to them that love
God, to them who are the called according to his purpose.
If we truly believe that verse, then we will understand that even the painful things that happen to us are in accordance with His will, and that He will use those things for good. Keeping that in mind helps us to avoid becoming bitter, it helps us to understand our relationship with Him. (He is God, we are merely created beings subject to His will), and it reminds us to trust Him, having Faith that He will keep His word. Most Christian denominations teach that trials and tribulation purifies us - they make us stronger. We should be thankful for that, as well. That's a bit harder to do.