Wireless Range Extender Issue

A wireless extender like that cuts your bandwidth in half and introduces increased latency because of the repeating it has to do.
Think of wireless Ethernet like a CB radio (or walkie-talkie). Only one person can talk at a time and you can only talk or listen at one time but not both. That is exactly how wireless network radios work. So if you have 5 devices in your house using your wireless that is like having 5 people using CB radio's together. Only one person can talk at a time. Lets say your neighbors also use CB radios. Lets say they use the same channel as your CB radio's. Lets say they also have 5 people talking. Now you can only talk when the other 9 people are not talking. This is how you get interference from your neighbors on WIFI networks if they are on the same channel. Now your Wifi is encrypted so your neighbors can't get your data. So for the CB analogy, lets say your neighbors use a language you cannot understand and you use one they can't understand. So your conversations are still private but you have to share CB airtime with them because they are on the same channel.
Now back to the original question. Why does repeating a wireless signal cut your bandwidth in half and introduce more latency, well back to the CB radio reference. To talk to someone on a CB you need to be on the same channel as them and talk their language (which on a wireless network to speak the "language" you need the SSID and password). So lets say I am in the middle with my radio. You are a mile to my west and the person you want to speak with is a mile to my east (so 2 miles from you). Your radio won't reach him but my radio can reach both of you. So you want to relay (repeat) your message through me to the guy at the far east. To hear you I have to be on your channel and talking your language. You tell me what to say and then I repeat it to the guy to my east. We are all on the same channel and talk the same language. Now since I have to repeat everything you say, it takes twice as long for you to talk to the guy to my east as it would if you could speak to him directly (because I have to relay it). This "delay" is what causes Wifi networks to cut the bandwidth in half (and introduce latency) in repeater mode.
But if you called me on the telephone (Ethernet cable between us) and told me what you wanted me to say, or even more if I held the CB up to the phone you could talk directly to the other guy and you would not have the delay associated with repeating. Thus when you wire your extender to your router you don't get your bandwidth cut in half as you do when repeating.
The CB radio is not a perfect example but it gives a person a very good idea of how wireless Ethernet works.