It's been ages since I watched an inconvenient truth. Your question is a little confusing but I assume you mean the Earth has warmed and cooled in the past on a regular basis. These are called the Milankovitch cycles. The Milankovitch cycles will change the weather on a regular basis over a longer period of time because of 3 things: the change in tilting of the axis of the Earth (obliquity), the wobbling of the axis (precession) and the stretching and squeezing of the eliptical orbit of the Earth. Just like the tilt of the Earth is responsible for the seasons, these three changes in the Earth's movement will cause changes in the weather as well but over a longer time (not exactly like seasons but you get the gist) leading to for example Ice Ages. Scientists know these orbital changes are not behind today's global warming because these parameters dictates we should be cooling now, not warming.
More info:
https://en.wikipedia.org/wiki/Milankovitch_cycles
I assume by that 10 year cycle you are referring to solar cycles. This is a periodic change in the Sun's activity with difference in output of radiation (among other things). Changes in solar radiation can cause a global temperature change because of an imbalance in energy, for example the energy changes in UV can have an influence on production and loss of ozone. Because the Sun is in a cooling trend the last decades while the Earth is getting warmer, scientists know the warmng of the Earth must have another source.
More info:
https://en.wikipedia.org/wiki/Solar_cycle
The Earth has indeed always known long periods of cooling and warming. Science is basically observing and describing, and if something doesn't add up scientist will search for an explanation. I wouldn't call it a desire. This suggests biased scientists want to point fingers at mankind ignoring other possibilities while in fact it has been a process of researching several hypotheses. Much like a crime scene with suspects where you have eventually one perpetrator. We know it's mankind. One of the reasons is CO2, in particular the isotopes of carbon: C12, C13 and C14.
The radioactive isotope Carbon-14 is produced in the upper layers of the stratosphere by collisions between neutrons and Nitrogen. It has a half life of about 5000-something years but atmospheric C14 gets replenished all the time so the concentration is fairly constant. C14 underground however does not get replenished. Man-made chemicals derived from fossil fuels (petroleum, coal, ...) will be greatly depleted of C14. It can therefore be used in measuring the relative contribution of this element tot the total C02 in a given region of the atmosphere. Meaning: when large quantities of CO2 from a long-buried source are added to the atmosphere it will result in a significant decline in C14 concentration. And this is what measurements shows: the source of the increased concentration of CO2 is fossil carbon, either from volcanoes or from fossil fuels. Studies however show that vulcanic eruptions are releasing only a fraction of human CO2 emissions.
C13 and C12 are stable isotopes. Plants will find it easier to take up more C12 than C13, and this differential intake can be used as an isotopic signature since the ratio of C12 and C13 in the atmosphere is different. It would also be different from the signature from CO2 from volcanoes and CO2 outgassing from oceans. In other words: if an increased level of C12 is found in the ratio C13/C12 in the atmospheric C02 it is very strong evidence that the CO2 is comming from burning of fossil fuels. And that is what they find.
Which brings me back to your question. Like you said the "Earth has always done this". Scientists know what impact it had on the planet by studying what happened. So it's important to know if (and that) it's man made and what the effects will be if mankind keeps going this course.