The argument is based on inference. First off, I am an independent Christian and while there are things that the very VAST MAJORITY of all Christians believe in regarding the faith, there may be some differences and disagreements among us. I am a independent Christian...and I do not belong to any church but I do confess that I am am sinner and that I accept by faith that Jesus Christ died on the cross for my sins, and it is to him that I am thankful and give praise to.
Now, with that being said...I don't know what kind of evidence that a creationist can provide...but I also don't know what kind of evidence an evolutionists can provide either. My only point from the get-go is the fact that based on what humans have observed throughout the history of human-kind, dogs have always produce dogs, cats-cats, etc. And what I am saying is, there is no REASON to believe that long ago, when no one else was around to see it, that things were otherwise different. I just don't see any reason to believe it...and I will go out on a limb and say that to be honest, I don't even think it is scientifically possible for such large scale-changes to occur in the first place.
Second, my personal belief system is that during the creation account, God may have created many different "original-kinds". So there may have been an original "house-cat" kind and all the small house cats that we see alive today are branches from that original kind...and the same applies for other different types of animals.
I admit, I believe this by faith...I can't prove it...but I just don't see any reasons to believe that such large scale changes such as macro-evolution has ever occurred, and until I can get an observation to go along with the theory, then as far as I'm concerned, macroevolution is a blatant lie and any Christian who believes in it is in error.