I think there is a lot more to it than "just" physical fitness/strength and the "bonding" issue.
sweeping generalisations alert based on own personal experience
Strength is a major one - the average Infantry Soldier carries around 35Kg of issued eqpt into battle, that's not including helmet, weapon, body armour and the personal items he finds useful. He could be carrying 50 Kgs and be expected to fight - that's a whole person! I am surrounded by soldiers and there are many males who struggle, and very few women (myself included) that would cope with that.
The main (most common) weapon for an infanteer is the Rifle 5.56, weighing about 4Kg, but different members of the same section carry different weapons - some a lot heavier - and the ammunition to go along with it. Plus the signaller would have the radio, the section medic the medical supplies and so on.
Women are also barred from the Armoured Corps, same issues, but with the added problem of Tanks. The driver of our most commonly used Armd Veh sits with his head in between the gunners legs - and its a tight fit. I don't know many women that would be willing to have their cheeks pressed against some blokes penis for hours on end - or days on end. Tanks go into 'lockdown' whereby no-one is allowed in or out, sometimes for days. The guys pee into plastic bottles and shite in bags - again, not many women I know would be comfortable with that - and what about periods - OK, you could fill yourself with hormones to make sure they didn't come - but should you have to?
Kit - "Webbing" is not designed well for women. It cuts directly across your breasts and sits on your hips. It's bad enough wearing it on exercise for a couple of weeks when you have plenty of time 'off' where you dont have to wear it - not going to happen in a war scenario.
Personally I think the British Army has the balance right. Women can go (and do go) to Front Line units and use their skills to their best advantage. Those that can, do. Those that can't, don't - and crucially aren't forced to do so. If the rules changed I believe less women would join or stay in the Army, not more.