The star-formation history (SFH) of galaxies is a key assumption to derive their physical properties and can lead to strong biases. In this work, we derive the SFH of main sequence (MS) galaxies and show how the peak SFH of a galaxy depends on its seed mass at, for example, z = 5. This seed mass reflects the galaxy’s underlying dark matter (DM) halo environment. We show that, following the MS, galaxies undergo a drastic slow down of their stellar mass growth after reaching the peak of their SFH. According to abundance matching, these masses correspond to hot and massive DM halos which state could result in less efficient gas inflows on the galaxies and thus could be the origin of limited stellar mass growth. As a result, we show that galaxies, still on the MS, can enter the passive region of the UVJ diagram while still forming stars. The best fit to the MS SFH is provided by a right skew peak function for which we provide parameters depending on the seed mass of the galaxy. The ability of the classical analytical SFHs to retrieve the star-formation rate (SFR) of galaxies from spectral energy distribution (SED) fitting is studied. Due to mathematical limitations, the exponentially declining and delayed SFH struggle to model high SFR, which starts to be problematic at z > 2. The exponentially rising and log-normal SFHs exhibit the opposite behavior with the ability to reach very high SFR, and thus model starburst galaxies, but they are not able to model low values such as those expected at low redshift for massive galaxies. By simulating galaxies SED from the MS SFH, we show that these four analytical forms recover the SFR of MS galaxies with an error dependent on the model and the redshift. They are, however, sensitive enough to probe small variations of SFR within the MS, with an error ranging from 5 to 40% depending on the SFH assumption and redshift; but all the four fail to recover the SFR of rapidly quenched galaxies. However, these SFHs lead to an artificial gradient of age, parallel to the MS, which is not exhibited by the simulated sample. This gradient is also produced on real data as we show using a sample of real galaxies with redshifts between 1.5 and 2.5. Here, we propose an SFH composed of a delayed form to model the bulk of stellar population with the addition of a flexibility in the recent SFH. This SFH provides very good estimates of the SFR of MS, starbursts, and rapidly quenched galaxies at all redshift. Furthermore, when used on the real sample, the age gradient disappears which show its dependency on the SFH assumption made to perform the SED fitting.