
was supposed to cut off

. Hané at the spot marked "good move",

is
nobi (extension) to save

, then Black connects at the 3-5 point in preparation for killing one or the other White group. In the actual game, your move made White's lower side group stronger. If after

at 2-5 White does not nobi, Black captures

with a play at 1-5 after playing at the 2-7 point.
Since there are only so many points on the board, as the number of stones increase there will be fights between opposing groups and cutting off enemy stones while rescuing your stones is an essential skill. If one side is going to get more points, it only follows that the other will lose points.
Beginners often struggle with analyzing capture situations. To capture stones or save them from capture, it is necessary to count on sight the number of liberties, or, more precisely, turns, available to two competing groups before capture occurs. Mastering the concept of liberties and capture is essential to understanding the concept of life & death, which is the category that deals with assessing whether a group of stones can be subject to capture or not and how to proceed towards the intended result. If a group of stones cannot be legally captured, it is considered to be "alive". If a group of stones is subject to legal capture at all times, then it is considered to be "dead". A group of stones is defined as any chain of stones solidly connected along orthogonal lines. There are techniques the beginner learns to increase the number of liberties available to his/her groups of stones, reduce the number of liberties available to the opponent's groups of stones, or both.
Below are a couple of model games to learn from. (COSUMI is playing at difficulty level 0 in both games.) This is a game in which Black wins by 10 points. Notice how Black did not attempt to attack White from the start.
Here, Black won by 3 points, despite making a mistake in reading out a capture by White. As well,

was to be at 9-4 instead of 7-1, as White can take advantage of the
kiri (cut) 6-5 and 7-6 to capture 2 Black stones. A couple more mistakes by Black appear in this game. I will let you think about them before giving my answer.
If you have a smartphone, I recommend downloading the Tsumego Pro app. It has hundreds of interactive Go puzzles and if, after several tries, you have difficulty getting the right answer, there is a feature indicated by a question mark (?) that you can press to be guided through the correct solution. Though, knowing the right answer is not as important as knowing
why the right answer is the right answer.
As you are just beginning to learn Go, there will be moments along the way when things get really hard and you feel like giving up. Well, I've learned that learning Go is like learning language. You learn individual bits such as phonemes and words in language, and individual moves such as shoulder hits, jumps, and attachments in Go, but each bit can be applied in a wide variety of contexts to derive meaning and so know how to proceed. Just as one word in a language can mean one thing in one context and quite another in another context, so can one particular move in Go have different implications in different contexts. Hopefully this can serve as brisk encouragement to persist in what can often be a heartbreaking game.