yes, absolutely can

"...moves with you..." key part there

This is one of my least favorite spells in terms of how little I understand how it is supposed to work and how absolutely useless it seems to be. You are relying on the enemy to have nothing but short-range melee options and no reinforcements to fetch. Even if you could corner a spell caster and trap them in antimagic, all anything has to do is improvise something it can throw at you to end your concentration.

Quote from NinjaTweak >>

This is one of my least favorite spells in terms of how little I understand how it is supposed to work and how absolutely useless it seems to be. You are relying on the enemy to have nothing but short-range melee options and no reinforcements to fetch. Even if you could corner a spell caster and trap them in antimagic, all anything has to do is improvise something it can throw at you to end your concentration.

 It is very effective against living enemies that are attacking with melee weapons only, without reach; or pretty much any creature that is attacking with parts of its body.  It does nothing against spells, or ranged attacks.  Reach itself may or may not work, as in the case of a bugbear, who is using a normal 5ft weapon and using its arms to increase to 10ft reach.  As it would require the arm to enter, it would be blocked.  But a giant, who would be using a giant-sized weapon, would probably be able to attack you.

Man, reading the comments. No one actually reads the spell, it's straight forward. You cast it, it extends in a radius around you. If you move causing the barrier to push into another creature it ends. This spell is more useful for blocking choke points or hallways to keep non-undead/constructs from reaching your allies while the range smoke them up. It's a control spell.

I simply do not understand this spell. Like I'm a smart guy, and have a complex job and this spell make no sense, and hedging out isn't clear enough to describe the action one must take if affected by this. neat sounding words, but ultimately one of the reasons I do not play a druid, its just a 5th level spell that makes no in game sense. 

 This is a restraining order from the lich, to the paladin.

Antilife Shell, or as I like to call it, Conjure Hamster Ball

Quote from SamsonSlice >>

Can the caster make a melee attack through it? (I want to say yes as I read "hedging out" as just preventing incoming direction and not outgoing direction)

So would this scenario work:

I cast Antilife shell on myself > Dragon tries to make a Claw, Bite, and Tail Attack > All attacks are repelled by the barrier even if the Tail attack has a reach of 15ft because it's not a weapon attack but is an extension of the Dragon's living body. Thoughts?

 The dragon's tail attack will not be able to hit you through the barrier, since the spell's description saysThe barrier prevents an affected creature from passing or reaching through. An affected creature can cast spells or make attacks with ranged or reach weapons through the barrier.  

If an enemy wields a polearm with at least 10 feet of reach they can hit you, but with natural weapons that are part of the enemy's body they cannot attack you.  However, the dragon can still breathe fire on you.  

It has to be able to make creatures move out of the way, otherwise it would end as soon as the field hits a bug, which would be pretty stupid.

"Forced" must refer to cases like where you push it into a corner with nowhere to go. Interpreting it as ending because you walk the barrier into a creature in the open makes the spell completely worthless as a moving field, which doesn't make sense given that the spell clearly implies that's it's supposed to be practical for it to move with you. It is a 5th level spell, so I don't think that makes it OP.

I rule it as being a shell that is 10' out from you and doesn't fill the intervening space.

Thus, creatures already within the 10' radius at the time of casting would not be pushed out of the way and could still attack you. If the creature is right at the 10' mark, I would say it is not hedged out as it is already partially in.

I also rule that it can make creatures move out of the way and that "forced" refers to something like backing them into a corner with nowhere to go, not just moving into their space. Otherwise, the spell would end as soon as you walk within 10' of a mouse or even a bug.