If your question is asking why does the stated material not constitute a good argument for the existence of God, the answer hinges upon the difference between propositions and propositional attitudes.
I think God exists, because I was raised a Baptist. The book states
that this wasn't an argument because it just stated a reason for why
they believed in God.
In short, arguing about 'God existing' and why 'belief exists about God's existence' are two distinct topics, and it seems that the authors may have been arguing that the text discusses the nature of the belief about God rather than God directly. Propositional attitudes are very important in understanding philosophical intentionality. In this case, the point is not about the nature of the structure of the argument, but rather about the relationship between belief and knowledge.
First, let's suss out the difference between belief and knowledge at an introductory level by examining justified, true belief (JTB) as a basis for knowledge which is an epistemological topic.
Certainly, belief in the existence of something doesn't necessarily imply the existence of something. Children are often led to believe in tooth fairies despite the lack of existence of tooth fairies. A parent who gives money in exchange for a tooth while a child sleeps is providing evidence to justify the existence to reinforce belief because even young children are attuned to the difference between reality and imagination. In fact, science provides strong evidence that psychological and philosophical belief are rooted in evolutionary principles. The ability to tell what and what not 'the state of affairs' is is a natural ability that is observable even in pre-speech infants who manifest object permanence. In fact, the debate over what is real and what is not, what exists and what doesn't is rooted in naive realism.
So, let's provide an argument to speak merely about the existence of God.
I talk to God and read the signs he gives, therefore God exists.
This is an implicit argument containing an enthymeme articulated below.
P1 I talk to God and read the signs he gives.
(P2 If I can talk to someone and they talk back, they exist.)
C Therefore, God exists.
(Note, some thinkers refuse to acknowledge the existence of implicit arguments based on the claim that one simply cannot draw conclusions about another's enthymemes. This is a deficient reading of argumentation if you have any familiarity with the cooperative principle and Gricean maxims and real-world communication.)
In this example, the argument, depending on your views of the premises may or not follow, but it's unavoidably an argument (implicit or otherwise). A person commits to ontological status, explicitly provides one premise, and is obviously situating those two statements amid what constitutes common-sensical notions about existence. Instead of good, let us recognize that arguments may be sound and valid or strong and cogent depending on your take of formal and informal argumentation.
But what the authors offer is an entirely different example, whereby the claimant seems to be making a claim about the existence of God based on their beliefs and their origins.
I think God exists, because I was raised a Baptist.
P1 I was raised Baptist.
(P2 Baptist beliefs are true about God's existence.)
C I think God exists.
This is a poor argument about God's existence not because it is an implicit argument which relies on enthymemes, but rather because it doesn't actually argue whether not exists but rather explains the origin of the belief.
This is subtle. To know God exists, one has to have adequate justification and true belief, and making the claim that the existence of God is predicated upon personal and social belief and its origins doesn't anything to directly argue the existence of God. After all, millions of children believe in the tooth fairy, and yet you'd be hard-pressed to find a defender of the reality of the tooth fairy. In fact, this argument seems to hinge upon argument by popularity or perhaps argument by authority. It is this lack of justification about God's existence that makes the argument poor in establishing the existence of God. This is why many theologians have gone to great lengths to build an argumentation to withstand refutation by naturalists. A good example is the ontological argument for the existence of God.
Ultimately, the important lesson to draw is that a gulf stands betweens belief and knowledge of existence, though what constitutes the appropriate bridge to establish the latter from the former is a matter of ontological debate especially since Edmund Gettier posed some simple questions with heavy logical consequence in the 1960's.