My husband and I agree on most things when it comes to raising our LO, but we seem to be butting heads some about whether we should do the "cry it out" method. I think we may actually want to do the same thing but there's some kind of misunderstanding. I am strongly opposed to crying it out; I go to my LO as soon as she cries in distress. She always needs something. She will fuss for a minute or two if I'm in the middle of something, but even while I am finishing up what I am doing, I talk to her from the other room.
My husband does the same thing, but he keeps mentioning that we should start letting her cry so she doesn't expect us to always pick her up whenever she wants. At first it sounded like he wanted to have her start crying it out ASAP, but we've discussed how babies aren't trying to manipulate you and need you to respond to them as quickly as possible when they are under 4 months. To me, crying it out means ignoring her crying until she stops. But when I ask him what exactly he wants to do, and ask him if he just wants us to ignore her crying, he says no. It sounds almost like he is afraid she is not going to learn how to be by herself. She is a little clingy, but she is very alert and gets upset being stuck on her back in a stationary place. She really likes us to hold and carry her all the time. It makes a lot of sense to me, I'd be bored and lonely just staring at the same thing and not able to move around. She will play in her activity gym for about 15 to 20 minutes before wanting us to take her out, that's about the only time she is okay being by herself on her back. I think her behavior is perfectly normal and I'm not worried she is learning something bad by us picking her up when she cries for us. I'm not sure what to do to help him understand she will be okay and we aren't going to have a bratty kid because we responded to her cries.

Re: Crying it out?
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When she's like that, we put her down, walk away, take 3 deep breaths, then if she's still crying we go back. On the occasion that she cries her hurt cry instead of her tired cry, we will not hesitate at all and get her right away.
This happens maybe once every couple of weeks, but it's letting her figure things out without her feeling abandoned.
OP - ditto PPs about doing research into normal infant development. The first year of life especially, babies need to be close to their parent. It's a need as much as eating/sleeping. You are doing a great thing by responding to your baby's needs whenever possible, and if baby is crying out for comfort, giving that to her will only lead to a happier, more independent child who knows her parents are there when she needs help.
I would also talk with your H about the source of his concerns. Why is he so worried about a 2-3m old having "bad habits" like depending on mom/dad? Although I would argue it's not a bad habit at all.