Let me try to answer your questions.
First, many professionals feel that when children have quality relationships with two parents, this is typically better than having it with just one. So unless you are suspicious that the father will almost certainly do your child more harm than good over time if they develop a relationship, the prospect of good things coming from allowing contact would probably make taking the risk of allowing visitation worthwhile for your child. It will be important to separate your own feelings of distress and displeasure with the father from what may be good for your child.
Related to the above point is that in the "abstract", there is probably no harm is granting visitation. That is, if he exercises the visitation right and things go well with the relationship that develops, fine; but naturally, if the rights are not exercised, nothing of course, will develop in the way of a relationship; and you and your child would have the same status with the father irrespective of whether you disallowed visitation or did
not----his behavior will make the relationship nonexistent, limited or of high quality. Of course, what you do not want to see happen is for this man to repeatedly jump in and out of this child's life, encouraging a strong attachment and then continually promising and not delivering on his promises thereafter. Anticipating time spent with an absent parent and then being disappointed time and time again is certainly not good for the child and if you allow visitation and start to see this happening, you should intervene aggressively to stop it (either through mediation or threatened/legal action against the father to change the status).
You are certainly wise enough to appreciate the fact that you really cannot determine in advance whether this man will follow through and take advantage of visitation rights and really step-up to be a good father---to the extent visitation allows. I think again, that most experts would suggest that unless the man has serious legal or antisocial behavior problems, drug addiction or other bad behavior you do not want a child exposed to, the child should be given some chance to form a relationship with both biological parents, and so, some visitation should be allowed. You note that he has shown virtually no interest in being with his child since the birth and therefore, the interest in visitation rights at this time seems to make no sense; technically, he has abandoned the child. Nonetheless, he may "step up" at this point and take on more responsibility to be a good father and this should perhaps be risked.
What you might want to do is tell the father that you want to meet together with a child or family psychologist or social worker to talk about visitation issues (agreements, rules, what should and should not happen with visitation) before you approve any visitation. Such a discussion can include an informal "contract", written up between the three of you regarding expectations and things he will and will not do e.g., have the child over while he is having a drinking party with his friends. Perhaps some initial visitations should be supervised until he proves himself. This activity can be very educational for the father, who may be naive about the time and energy being a proper father must take. Maybe he would agree to take a parenting class alone or with you. Just some examples here. So, he may well know very little about fathering. Such a session with a third party can tutor him indirectly, just a bit. But agreement will allow you to come back in the future and identify specific failures you informally agreed upon, if he fails to meet basic responsibilities. Though it is not a legal document, it can be shared with the court in the future if need be, as data on what was agreed upon, and what failed or did not fail.
Hope this information is helpful to you. If I have failed to answer your question adequately, please let me know.
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