Rather than start by pointing out the problems with this objection, I would rather take it at face value and see where it leads me. If God sends people to Hell, then He is not good and loving. Okay, let's work with that. Now, before we dive into the deep end, please understand that I am working with this objection and only this objection here. I understand that there are a lot of related issues, but I do not have space to address them all in this space. Furthermore, I am taking it on its own terms, which requires at least the possibility that God exists (e.g. If God exists then...). Otherwise, the objection is just nonsense--akin to saying, "The tooth fairy is a jerk because she is always stealing children's teeth." With that preface, here is my train of thought.
What if God didn't send people to Hell? Presumably that would be good and loving, and eliminate the problem. For the moment, ignore everything that is wrapped up in that question, such as the biblical teaching on Hell, the historical Christian teachings on Hell etc. Dump your brain for a second and try to imagine an alternate universe where God exists and human beings exist but God does not send any of them to Hell (which is a noun that doesn't exist in this universe, so we will just say that God doesn't punish anyone). Would that be a world where no one calls God's goodness and love into question? I don't think so.
The way I see it, there are only a couple of ways that such a universe could exist (where both God and humans). Either God could deprive humans of moral freedom (which minimally allows for the possibility of evil), or He could simply refrain from punishing evil (e.g. sending people to Hell). The former hardly seems worth discussing. Even so, if it were possible for even one man from our universe to be transported to that alternate plane, inhabited entirely by fleshly automatons, I do not imagine that he would necessarily judge it better than our own. Superficially better? Perhaps. But it would also be a world without the capacity for love. After all, love that is programmed or forced is not love. My mind can barely begin to conceive of just how empty, and frankly, not good, such an existence would seem for an observer who has experienced freedom and love. He would certainly wonder how a good and loving God could create a world where human beings exist without the ability to give and receive love. Would he not conclude that "God does X, and X is not good and loving; therefore, God is not good and loving," where X equals: "creates humans without freedom to love"?
The other option, and this seems to be the one that opponents of Christianity favor, is that God would simply refrain from punishing evil. Once again, do a brain dump and try to imagine an alternate universe where God exists and human beings are free to do evil, but do not face divine punishment. Would everyone in that world agree that God is good and loving? What about the person whose loved ones were brutally murdered? There can be no doubt that they would object to God's goodness in precisely the same way as do people in our world--"God does X, and X is not good and loving; therefore, God is not good and loving." The only difference is that in this case, X is "refrains from punishing evil." It is exactly the opposite of the objection raised in our world. God is not good and loving because He does not punish evil (e.g. send people to Hell). How can this be? It seems that God is, and forgive the pun, damned if He does and damned if He doesn't.
At this point, I can imagine that someone might say, "Well, of course a good and loving God (if He exists) would punish the really egregious evils like murder, rape, and the like. The part that is objectionable is the fact that He would punish people for minor stuff." This position hardly seems tenable. It is tantamount to saying, "I only want God to punish the stuff that I deem worthy." Furthermore, I have written elsewhere about the logical problem with cherry picking certain evils and saying "If God allows THAT, then He isn't good, and I won't worship Him." You can read that full article here.*
In this space I have simply endeavored to show that the objection, "A good and loving God wouldn't send anyone to Hell" is not a very good one. If the exact opposite were true--if we lived in a universe where God did not punish evil--then the same objection (only the inverse) would almost certainly be raised. This demonstrates that it is just a smokescreen for the claim, "If I were God, I would do it differently." That is fine, but inasmuch as it has nothing to do with the objection itself, the objection has no real substance.
*Do not think that I am unaware of the doctrinal questions that arise concerning the nature of eternal punishment. I am well aware of the objection that says "eternal damnation is obvious overkill for a finite amount of evil." As I said in the preface to this point, I do not have space to address every related issue. Even so, I am open to dealing with this particular question in a future article.