Are men allowed to hit woman?
It is possible and most likely that the word اضْرِبُوهُنَّ is miss-translated to beat or hit while it also has other meanings such "separate/Isolate" as pointed out in verse 13 below from Surat Al-Hadid
يَوْمَ يَقُولُ الْمُنَافِقُونَ وَالْمُنَافِقَاتُ لِلَّذِينَ آمَنُوا
انظُرُونَا نَقْتَبِسْ مِن نُّورِكُمْ قِيلَ ارْجِعُوا وَرَاءكُمْ
فَالْتَمِسُوا نُورًا فَضُرِبَ بَيْنَهُم بِسُورٍ لَّهُ بَابٌ بَاطِنُهُ
فِيهِ الرَّحْمَةُ وَظَاهِرُهُ مِن قِبَلِهِ الْعَذَابُ
On the Day when the hypocrites men and women will say to the
believers: "Wait for us! Let us get something from your light!" It
will be said: "Go back to your rear! Then seek a light!" So a wall
will be put up between them, with a gate therein. Inside it will be
mercy, and outside it will be torment."
The word is yet again mentioned in another verse with a different meaning:
O ye who believe! When ye go abroad (darabtum) In the cause of Allah,
Investigate carefully, And say not to anyone Who offers you a
salutation: 'Thou art none of a Believer!' Coveting the perishable
good Of this life: with Allah Are profits and spoils abundant. Even
thus were ye yourselves Before, till Allah conferred On you His
favours: therefore Carefully investigate. For Allah is well aware Of
all that ye do. (The Noble Quran, 4:94)
Have a look at this site here
The Prophet (peace and blessings of Allaah be upon him) said: “The
best of you are those who are the best to their wives, and I am the
best of you to my wives.” Narrated by al-Tirmidhi, 3895; Ibn Maajah,
1977; classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
The value of sincerety is emphasised over and over again in both the quran and sunnah, so there is no value in doing something which you aren't sincere in:
"Verily, all actions are but driven by intention and for everyone is
what he intended."[Al-Bukhari and Muslim]
Are men responsible over woman?
You also asked about why are Men responsible over women, which I believe is derived from this verse:
“Men are the protectors and maintainers of women because of what Allah
has preferred one with over the other and because of what they spend
to support them from their wealth.” [Sûrah al-Nisâ’: 34]
Yet again the word "Qawammun" is also sorrounded with a difference of opinion, as some may translate it to "Protecters or Gaurdians" and other may translate it by "Responsible over"
To address the view that translates the word as "Protector/Guardian/Affair manager" you can't expect your wife to fight an intruder/offender while she is pregnant, therefore it is your duty to act as a guardian/protector/provider.
Think about the main responsibilities of women in the past, these where to take care of their children and raise them while men used to go and hunt to provide food or earn a living to also participate in raising children, it is a shared responsibility, some affairs can only be accomplished by women (Breast feeding, pregnancy), some responsibilities may be more demanding and restrictive than others (this is often the woman's) and that's when aid comes in from the other side (from men), for example you cant expect your wife to go hunt and gather wood while pregnant or breast feeding therefore you aid her, you reduce some load of her by managing her affairs.
Some translate it as "Responsible over them" and that you should make all decisions on behalf of them, Not sure about this view, as we each bare the consequences of our decision, for example those who obeyed their masters to disobey Allah cannot use that as a valid excuse to be saved from the hell fire:
And they will say, "Our Lord, indeed we obeyed our masters and our
dignitaries, and they led us astray from the [right] way. 33:67
We shouldn't make decisions that affect others without consulting them in the first place:
And those who have responded to their lord and established prayer and
whose affair is [determined by] consultation among themselves, and
from what We have provided them, they spend.
How to explain this verse to a female christian?
When speaking to non-Muslims bare in mind that they don't always have the background knowledge to understand certain concepts (I.E they may not know what the Quran or Hadith is), if you are not absolutely sure about something they ask, then ask a scholar to speak to them instead of you so you don't accidentally lead them in the wrong direction, don't feel embarrassed and let your ego tell you otherwise no one knows everything beside God.
I am no scholar I am just sharing what I found out about those topics and have tried to summarise different opinions, and add examples based on my own understanding. I could be wrong, Allah the knower of all things knows best!
I came across many Hadiths some opposing each other, As I am not a scholar and have insufficient knowledge to verify a Hadith I can't quote them or say which one is true and which is false, you can find a compilation of them here on the same site there is also various definitions of the word "Daraba" (Often translated to beat) along with a detailed study about the topic presenting both side of the argument here.
Considering what I've mentioned above, you've probably seen that if those who support a single view they will quote the Hadiths that support one side of the argument and leave out others, in my answer above I presented different arguments on the topic and if I have refuted something then I have justified why rather than turning a blind eye to others opinions.
I am still in the process of looking up scholars that address both sides of the argument rather than just support one and provide a detailed explanation rather than saying it is permissible or not
I still stand by my opinion, as I base my opinions based on that which is contrary to the basic and general teachings of Islam and by that which is backed by logic and wisdom
Did you think that We had created you in play (without any purpose),
and that you would not be brought back to Us?" 23:115
Bare in mind that unfortunately culture is often valued over religion, and often people attempt to justify their culture practices by religion, while it should be religion that influences culture not the opposite, as religion dictates how one should go about his all his daily affairs, but with little observation you'll realise that people often separate religion from life, for example someone may turn up to Friday prayers but block someones driveway just so they could park near by!